Slides of the talk
... T HEOREM (S YLOW (1832 - 1918)) Let G be a finite group and write |G| = mpn where p is a prime and m is not divisible by p. G contains a subgroup P of order pn . P is called “Sylow p-subgroup” of G. G contains a subgroup of order pk for every 0 ≤ k ≤ n. If P, Q are two Sylow p-subgroups of G then th ...
... T HEOREM (S YLOW (1832 - 1918)) Let G be a finite group and write |G| = mpn where p is a prime and m is not divisible by p. G contains a subgroup P of order pn . P is called “Sylow p-subgroup” of G. G contains a subgroup of order pk for every 0 ≤ k ≤ n. If P, Q are two Sylow p-subgroups of G then th ...
SIMPLE AND SEMISIMPLE FINITE DIMENSIONAL ALGEBRAS Let
... in Exercise 4. Let us first observe that the third condition is inherited by submodules: if N 0 is a submodule of a submodule M 0 , and P is a submodule such that M = N 0 ⊕ P , then M 0 = N 0 ⊕ (P ∩ M 0 ). Now proceed by induction on the dimension of M . Choose a simple submodule of N of M (which ex ...
... in Exercise 4. Let us first observe that the third condition is inherited by submodules: if N 0 is a submodule of a submodule M 0 , and P is a submodule such that M = N 0 ⊕ P , then M 0 = N 0 ⊕ (P ∩ M 0 ). Now proceed by induction on the dimension of M . Choose a simple submodule of N of M (which ex ...
CLUSTER ALGEBRAS AND CLUSTER CATEGORIES
... • commutative and non commutative algebraic geometry and in particular the study of stability conditions in the sense of Bridgeland [13], Calabi-Yau algebras [66, 57], Donaldson-Thomas invariants [106, 68, 82, 81, 95, 47, 46, 21, 48] . . . ; • and in the representation theory of quivers and finite-d ...
... • commutative and non commutative algebraic geometry and in particular the study of stability conditions in the sense of Bridgeland [13], Calabi-Yau algebras [66, 57], Donaldson-Thomas invariants [106, 68, 82, 81, 95, 47, 46, 21, 48] . . . ; • and in the representation theory of quivers and finite-d ...
Weighted semigroup measure algebra as a WAP-algebra H.R. Ebrahimi Vishki, B. Khodsiani, A. Rejali
... almost periodic elements of A∗ . It is easy to verify that, W AP (A) is a (norm) closed subspace of A∗ . It is known that the multiplication of a Banach algebra A has two natural but, in general, different extensions (called Arens products) to the second dual A∗∗ each turning A∗∗ into a Banach algebr ...
... almost periodic elements of A∗ . It is easy to verify that, W AP (A) is a (norm) closed subspace of A∗ . It is known that the multiplication of a Banach algebra A has two natural but, in general, different extensions (called Arens products) to the second dual A∗∗ each turning A∗∗ into a Banach algebr ...
CLASSIFICATION OF PRINCIPAL BUNDLES AND LIE GROUPOIDS
... Q : G + Aut(A) by e(g) = Ih IA, the restriction to A of the inner automorphism Zh of H corresponding to any h with rr(h) = g. If one now replaces A by an arbitrary group N and considers an extension ...
... Q : G + Aut(A) by e(g) = Ih IA, the restriction to A of the inner automorphism Zh of H corresponding to any h with rr(h) = g. If one now replaces A by an arbitrary group N and considers an extension ...
Moduli Problems for Ring Spectra - International Mathematical Union
... k-morphism in C is invertible. If X is any topological space, then the n-category π≤n X is an example of an n-groupoid: for example, the 1-morphisms in π≤n X are given by paths p : [0, 1] → X, and every path p has an inverse q (up to homotopy) given by q(t) = p(1 − t). In fact, all n-groupoids arise ...
... k-morphism in C is invertible. If X is any topological space, then the n-category π≤n X is an example of an n-groupoid: for example, the 1-morphisms in π≤n X are given by paths p : [0, 1] → X, and every path p has an inverse q (up to homotopy) given by q(t) = p(1 − t). In fact, all n-groupoids arise ...
The Essential Dimension of Finite Group Schemes Corso di Laurea Magistrale in Matematica
... Remark 1.5. This is particularly important since most algebraic stucture of interest are determined by maps between tensor products. This allows us to extend our descent theorem to other algebraic categories. For instance below we work out explicitely the case of algebras.1 Note that all equational ...
... Remark 1.5. This is particularly important since most algebraic stucture of interest are determined by maps between tensor products. This allows us to extend our descent theorem to other algebraic categories. For instance below we work out explicitely the case of algebras.1 Note that all equational ...
The Critical Thread:
... bases, and some knowledge about matrices. • Lie Representations: Much if not all of the knowledge from Galois Theory, vector spaces, vector subspaces, linear independence/dependence, bases, eigenvalues, bilinear forms, euclidean spaces, some tensor products, algebras. Though not necessary, it is als ...
... bases, and some knowledge about matrices. • Lie Representations: Much if not all of the knowledge from Galois Theory, vector spaces, vector subspaces, linear independence/dependence, bases, eigenvalues, bilinear forms, euclidean spaces, some tensor products, algebras. Though not necessary, it is als ...
FILTERED MODULES WITH COEFFICIENTS 1. Introduction Let E
... of (Cp ⊗Qp E)-modules (where the Gp -action is Cp -semi-linear and E-linear). The integers i such that (Cp ⊗Qp V ){i} = 6 0, counted with multiplicity dimE (Cp ⊗Qp V ){i}, are by definition the Hodge-Tate weights of the representation V . It is known by the fundamental work of Colmez and Fontaine [C ...
... of (Cp ⊗Qp E)-modules (where the Gp -action is Cp -semi-linear and E-linear). The integers i such that (Cp ⊗Qp V ){i} = 6 0, counted with multiplicity dimE (Cp ⊗Qp V ){i}, are by definition the Hodge-Tate weights of the representation V . It is known by the fundamental work of Colmez and Fontaine [C ...
On bimeasurings
... correspond to bialgebra maps from C to B(B, A) as well as bialgebra maps from B to B(C, A). In fact Bialg(C, B(B, A)) Bimeas(C ⊗ B, A) Bialg(B, B(C, A)) and hence the functor B( _, A) on the category of bialgebras is adjoint to itself. In the special case A = k, this gives a new proof that the fi ...
... correspond to bialgebra maps from C to B(B, A) as well as bialgebra maps from B to B(C, A). In fact Bialg(C, B(B, A)) Bimeas(C ⊗ B, A) Bialg(B, B(C, A)) and hence the functor B( _, A) on the category of bialgebras is adjoint to itself. In the special case A = k, this gives a new proof that the fi ...
CLASSIFICATION OF SEMISIMPLE ALGEBRAIC MONOIDS
... Z = T c E (Zariski closure) is an affine, torus embedding and G c E is a reductive, algebraic group. Torus embeddings have been introduced by Demazure in [6] in his study of Cremona groups, and are classified numerically using rational, polyhedral cones [14]. On the other hand, reductive groups have ...
... Z = T c E (Zariski closure) is an affine, torus embedding and G c E is a reductive, algebraic group. Torus embeddings have been introduced by Demazure in [6] in his study of Cremona groups, and are classified numerically using rational, polyhedral cones [14]. On the other hand, reductive groups have ...
Serial Categories and an Infinite Pure Semisimplicity Conjecture
... Locally finite categories More generally, one can consider a finitely accessible K-linear category with where simple modules are finite dimensional. I.e. objects are locally finite. Such categories have also been called of finite type. • lf.A-Mod = locally finite A-modules over an algebra A. Not ev ...
... Locally finite categories More generally, one can consider a finitely accessible K-linear category with where simple modules are finite dimensional. I.e. objects are locally finite. Such categories have also been called of finite type. • lf.A-Mod = locally finite A-modules over an algebra A. Not ev ...
ASSOCIATIVE GEOMETRIES. I: GROUDS, LINEAR RELATIONS
... an associative product xy really gives rise to a family of associative products x ·a y := xay for any fixed element a, called the a-homotope. Therefore we should rather expect to deal with a whole family of Lie groups, instead of looking just at one group corresponding to the choice a = 1. 0.1. Gras ...
... an associative product xy really gives rise to a family of associative products x ·a y := xay for any fixed element a, called the a-homotope. Therefore we should rather expect to deal with a whole family of Lie groups, instead of looking just at one group corresponding to the choice a = 1. 0.1. Gras ...
Applying Universal Algebra to Lambda Calculus
... Barendregt’s book [4]). At the beginning researchers have focused their interest on a limited number of equational extensions of lambda calculus, called λ-theories. They arise by syntactical or semantic considerations. Indeed, a λ-theory may correspond to a possible operational semantics of lambda c ...
... Barendregt’s book [4]). At the beginning researchers have focused their interest on a limited number of equational extensions of lambda calculus, called λ-theories. They arise by syntactical or semantic considerations. Indeed, a λ-theory may correspond to a possible operational semantics of lambda c ...
Chapter 9 Lie Groups, Lie Algebras and the Exponential Map
... Let us also recall the definition of homomorphisms of Lie groups and Lie algebras. Definition 9.3. Given two Lie groups G1 and G2, a homomorphism (or map) of Lie groups is a function, f : G1 ! G2, that is a homomorphism of groups and a smooth map (between the manifolds G1 and G2). Given two Lie alge ...
... Let us also recall the definition of homomorphisms of Lie groups and Lie algebras. Definition 9.3. Given two Lie groups G1 and G2, a homomorphism (or map) of Lie groups is a function, f : G1 ! G2, that is a homomorphism of groups and a smooth map (between the manifolds G1 and G2). Given two Lie alge ...
Dual Banach algebras
... If E is a reflexive Banach space with the approximation property, then B(E) is Connes-amenable if and only if K (E), the algebra of compact operators, is amenable. So B(`p ) is Connes-amenable for 1 < p < ∞. ...
... If E is a reflexive Banach space with the approximation property, then B(E) is Connes-amenable if and only if K (E), the algebra of compact operators, is amenable. So B(`p ) is Connes-amenable for 1 < p < ∞. ...
Full text
... for a natural algebraic and geometric setting for their analysis. In this way many known results are unified and simplified and new results are obtained. Some of the results extend to Fibonacci representations of higher order, but we do not present these because we have been unable to extend the the ...
... for a natural algebraic and geometric setting for their analysis. In this way many known results are unified and simplified and new results are obtained. Some of the results extend to Fibonacci representations of higher order, but we do not present these because we have been unable to extend the the ...
LECTURES ON ERGODIC THEORY OF GROUP ACTIONS (A VON
... An action of a discrete group Γ on the standard probability space (X, µ) is a group σ morphism σ : Γ → Aut(X, µ). We’ll often use the notation Γ y (X, µ) to emphasize an action σ, or simply Γ y X if no confusion is possible. We’ll sometimes consider topological groups G other than discrete (typicall ...
... An action of a discrete group Γ on the standard probability space (X, µ) is a group σ morphism σ : Γ → Aut(X, µ). We’ll often use the notation Γ y (X, µ) to emphasize an action σ, or simply Γ y X if no confusion is possible. We’ll sometimes consider topological groups G other than discrete (typicall ...
Problems in the classification theory of non-associative
... A, x 7→ ax and Ra : A → A, x 7→ xa are invertible for all non-zero a ∈ A. In finite dimension, this condition is equivalent to the non-existence of zero-divisors, i.e., xy = 0 only if x = 0 or y = 0. The focus in the present thesis, as well as in most articles written on the subject, is on the case ...
... A, x 7→ ax and Ra : A → A, x 7→ xa are invertible for all non-zero a ∈ A. In finite dimension, this condition is equivalent to the non-existence of zero-divisors, i.e., xy = 0 only if x = 0 or y = 0. The focus in the present thesis, as well as in most articles written on the subject, is on the case ...
DEFINING RELATIONS OF NONCOMMUTATIVE ALGEBRAS
... In commutative algebra Gröbner bases have proved their efficiency and are applied as a powerful tool in the study of many related fields as invariant theory and algebraic geometry. The noncommutative Gröbner bases are more recent objects of investigations but nevertheless they also have a lot of a ...
... In commutative algebra Gröbner bases have proved their efficiency and are applied as a powerful tool in the study of many related fields as invariant theory and algebraic geometry. The noncommutative Gröbner bases are more recent objects of investigations but nevertheless they also have a lot of a ...
Small Deformations of Topological Algebras Mati Abel and Krzysztof Jarosz
... In this paper we extend the theory of small deformations to topological algebras. There are several ways to generalize the definition of a small deformation into the class of algebras equipped with a topology but without a norm. In the two sections following the Definitions and Notation we discuss two ...
... In this paper we extend the theory of small deformations to topological algebras. There are several ways to generalize the definition of a small deformation into the class of algebras equipped with a topology but without a norm. In the two sections following the Definitions and Notation we discuss two ...
http://homes.dsi.unimi.it/ ghilardi/allegati/dispcesena.pdf
... These notes cover the content of a basic course in propositional algebraic logic given by the author at the italian School of Logic held in Cesena, September 18-23, 2000. They are addressed to people having few background in Symbolic Logic and they are mostly intended to develop algebraic methods fo ...
... These notes cover the content of a basic course in propositional algebraic logic given by the author at the italian School of Logic held in Cesena, September 18-23, 2000. They are addressed to people having few background in Symbolic Logic and they are mostly intended to develop algebraic methods fo ...
GENERIC SUBGROUPS OF LIE GROUPS 1. introduction In this
... to solvability it follows from the “Tits alternative” (see [15]). Thus we only have to show, that given a non-nilpotent connected Lie group G, there exists a subgroup with 2 generators which is not nilpotent. Since G is not nilpotent, Ado’s theorem implies that there is an element v in the Lie algeb ...
... to solvability it follows from the “Tits alternative” (see [15]). Thus we only have to show, that given a non-nilpotent connected Lie group G, there exists a subgroup with 2 generators which is not nilpotent. Since G is not nilpotent, Ado’s theorem implies that there is an element v in the Lie algeb ...
SCARCITY AND ABUNDANCE OF TRIVIAL ZEROS IN DIVISION
... Here we shall be concerned with possible trivial zeros at s = 1 of twisted L-functions of an elliptic curve, the twists being self-dual Artin representations of the Galois group of a division tower of the curve. The reason for restricting attention to selfdual representations is that the conjectural ...
... Here we shall be concerned with possible trivial zeros at s = 1 of twisted L-functions of an elliptic curve, the twists being self-dual Artin representations of the Galois group of a division tower of the curve. The reason for restricting attention to selfdual representations is that the conjectural ...
On the Associative Nijenhuis Relation
... Hoffman’s quasi-shuffle product [16] is new. For a detailed account of the link between the mixable and quasi-shuffle product, also addressing Hopf algebraic aspects, we refer the reader to the results in the recent work [11]. The essential point (for both constructions of the free objects) lies in ...
... Hoffman’s quasi-shuffle product [16] is new. For a detailed account of the link between the mixable and quasi-shuffle product, also addressing Hopf algebraic aspects, we refer the reader to the results in the recent work [11]. The essential point (for both constructions of the free objects) lies in ...