booklet of abstracts - DU Department of Computer Science Home
... In Group Theory there has been a lot of research on the properties of groups given the geometric and combinatorial properties of their Cayley graphs. More recently, thanks to the works of mathematicians like G. Sabidoussi, G. Gauyacq and E. Mwambené, it has been possible to define and study the Cay ...
... In Group Theory there has been a lot of research on the properties of groups given the geometric and combinatorial properties of their Cayley graphs. More recently, thanks to the works of mathematicians like G. Sabidoussi, G. Gauyacq and E. Mwambené, it has been possible to define and study the Cay ...
Basics of associative algebras
... in R) if (i) I is a group under addition, (ii) RI ⇢ I, and (iii) IR ⇢ I. If we only require that I satisfy (i) and (ii), we say I is a left ideal of R. Similarly, if we only require I satisfy (i) and (iii), we say I is a right ideal of R. A left or right ideal is called a onesided ideal. Of course t ...
... in R) if (i) I is a group under addition, (ii) RI ⇢ I, and (iii) IR ⇢ I. If we only require that I satisfy (i) and (ii), we say I is a left ideal of R. Similarly, if we only require I satisfy (i) and (iii), we say I is a right ideal of R. A left or right ideal is called a onesided ideal. Of course t ...
Relational Algebra
... R(A1, A2, …., An) and S(B1, B2, …, Bn) is UNION compatible if dom(Ai) = dom(Bi) for 1 i n. ==> two relations have the same number of attributes and that each pair of corresponding attributes have the ...
... R(A1, A2, …., An) and S(B1, B2, …, Bn) is UNION compatible if dom(Ai) = dom(Bi) for 1 i n. ==> two relations have the same number of attributes and that each pair of corresponding attributes have the ...
Real banach algebras
... Theorem 3.6 on real normed division algebras we give a complete proof whose algebraic part is self-contained and elementary. In the last part (sec. 4) of the chapter the real counterpart of the Gelfand representation theory [11] for commutative complex Banach algebras is presented. All the material ...
... Theorem 3.6 on real normed division algebras we give a complete proof whose algebraic part is self-contained and elementary. In the last part (sec. 4) of the chapter the real counterpart of the Gelfand representation theory [11] for commutative complex Banach algebras is presented. All the material ...
Lectures on Hopf algebras
... These notes contain the material presented in a series of five lectures at the University of Córdoba in September 1994. The intent of this brief course was to give a quick introduction to Hopf algebras and to prove as directly as possible (to me) some recent results on finitedimensional Hopf algebr ...
... These notes contain the material presented in a series of five lectures at the University of Córdoba in September 1994. The intent of this brief course was to give a quick introduction to Hopf algebras and to prove as directly as possible (to me) some recent results on finitedimensional Hopf algebr ...
An efficient algorithm for computing the Baker–Campbell–Hausdorff
... processor with 2 Gbytes of random access memory兲 requires less than 15 min of CPU time and 1.5 Gbytes of memory. The resulting expression has 109 697 nonvanishing coefficients out of 111 013 elements Ei of degree 兩i兩 艋 20 in the Hall basis. As far as we know, there are no results up to such a high d ...
... processor with 2 Gbytes of random access memory兲 requires less than 15 min of CPU time and 1.5 Gbytes of memory. The resulting expression has 109 697 nonvanishing coefficients out of 111 013 elements Ei of degree 兩i兩 艋 20 in the Hall basis. As far as we know, there are no results up to such a high d ...
Lie algebra cohomology and Macdonald`s conjectures
... is called trivial.) The only element of V that is fixed by all ρ(X) is 0, for ρ(0) = 0. Yet there is a notion of g-invariant vectors. Namely, an element v of V is g-invariant if ∀X ∈ g : ρ(X)v = 0. Later on it will become clear why this is a reasonable definition. These invariants also form a g-subm ...
... is called trivial.) The only element of V that is fixed by all ρ(X) is 0, for ρ(0) = 0. Yet there is a notion of g-invariant vectors. Namely, an element v of V is g-invariant if ∀X ∈ g : ρ(X)v = 0. Later on it will become clear why this is a reasonable definition. These invariants also form a g-subm ...
The Classification of Three-dimensional Lie Algebras
... where w := α−1 y and hence L = F w + F z is a Lie algebra such that L0 = F z. By construction it is clear that this is the only non-abelian two-dimensional Lie algebra up to isomorphism. The two-dimensional Lie algebra of type (b) will be of particular interest later on and for this reason shall be ...
... where w := α−1 y and hence L = F w + F z is a Lie algebra such that L0 = F z. By construction it is clear that this is the only non-abelian two-dimensional Lie algebra up to isomorphism. The two-dimensional Lie algebra of type (b) will be of particular interest later on and for this reason shall be ...
Morita equivalence for regular algebras
... In this section we generalize to regular algebras some classical consequences of the Eilenberg-Watts theorem. First of all, let us restate it in the more meaningful language of bicategories (cf. [6]). We write Algreg for the bicategory whose objects are regular algebras, whose 1-arrows are regular b ...
... In this section we generalize to regular algebras some classical consequences of the Eilenberg-Watts theorem. First of all, let us restate it in the more meaningful language of bicategories (cf. [6]). We write Algreg for the bicategory whose objects are regular algebras, whose 1-arrows are regular b ...
AN INTRODUCTION TO FLAG MANIFOLDS Notes1 for the Summer
... O(n) = {g ∈ Matn×n (R) : g · g T = I}, so O(n) is a Lie group. It is not connected: indeed, its subgroup SO(n) := {g ∈ O(n) : det(g) = 1} is connected (use the same connectivity argument as for U(n), see above) and O(n) is the disjoint union of SO(n) and O − (n) := {g ∈ O(n) : det(g) = −1}. The grou ...
... O(n) = {g ∈ Matn×n (R) : g · g T = I}, so O(n) is a Lie group. It is not connected: indeed, its subgroup SO(n) := {g ∈ O(n) : det(g) = 1} is connected (use the same connectivity argument as for U(n), see above) and O(n) is the disjoint union of SO(n) and O − (n) := {g ∈ O(n) : det(g) = −1}. The grou ...
Splittings of Bicommutative Hopf algebras - Mathematics
... ring K(n)∗ ' Fp [vn±1 ] where p is a prime and the degree of vn is 2(pn − 1). The first two authors were led by their study [KL02] to an interest in the fibration K(Z, 3) → BOh8i → BSpin. The Morava K-theory for p = 2 of this was analyzed in [KLW]. In particular, for n = 2, although the first map do ...
... ring K(n)∗ ' Fp [vn±1 ] where p is a prime and the degree of vn is 2(pn − 1). The first two authors were led by their study [KL02] to an interest in the fibration K(Z, 3) → BOh8i → BSpin. The Morava K-theory for p = 2 of this was analyzed in [KLW]. In particular, for n = 2, although the first map do ...
A MONOIDAL STRUCTURE ON THE CATEGORY OF
... have been discussed in [5], in the particular case where C is the category of vector spaces over a field k. A monoidal structure on B CA can be constructed if A is a bialgebra and two additional compatibility conditions are satisfied. The aim of this paper is to present a more general result in the ...
... have been discussed in [5], in the particular case where C is the category of vector spaces over a field k. A monoidal structure on B CA can be constructed if A is a bialgebra and two additional compatibility conditions are satisfied. The aim of this paper is to present a more general result in the ...
power-associative rings - American Mathematical Society
... simple algebras. The final line of investigation we shall present here is a complete determination of those algebras 21 such that 2I(+) is a simple Jordan algebra. We are first led to attach to any algebra 33 over a field % an algebra 33(X) defined for every X of %. This algebra is the same vector s ...
... simple algebras. The final line of investigation we shall present here is a complete determination of those algebras 21 such that 2I(+) is a simple Jordan algebra. We are first led to attach to any algebra 33 over a field % an algebra 33(X) defined for every X of %. This algebra is the same vector s ...
nearly associative - American Mathematical Society
... One verifies easily that if the subscripts here are interpreted modulo 7, every possible product of basis elements is defined exactly once by these equations. It is also clear that for each value of i the elements 1, ei9 ei+l9 ei+3 span a subalgebra which is isomorphic to the quaternions. Once the o ...
... One verifies easily that if the subscripts here are interpreted modulo 7, every possible product of basis elements is defined exactly once by these equations. It is also clear that for each value of i the elements 1, ei9 ei+l9 ei+3 span a subalgebra which is isomorphic to the quaternions. Once the o ...
Problems in the classification theory of non-associative
... spanned by vectors 1, i, j and k, with multiplication determined by bilinearity and Table 1.1. ...
... spanned by vectors 1, i, j and k, with multiplication determined by bilinearity and Table 1.1. ...
Boolean Algebra
... totally symmetric), if and only if it is invariant under any permutation of its variables. It is partially symmetric in the variables Xi,Xj where {Xi,Xj} is a subset of {X1,X2…Xn} if and only if the interchange of the variables Xi,Xj leaves the function ...
... totally symmetric), if and only if it is invariant under any permutation of its variables. It is partially symmetric in the variables Xi,Xj where {Xi,Xj} is a subset of {X1,X2…Xn} if and only if the interchange of the variables Xi,Xj leaves the function ...
Classical Yang-Baxter Equation and Its Extensions
... Let g be a Lie algebra. Let ρ : g → gl(V ) be a representation of g and ρ∗ : g → gl(V ∗ ) be the dual representation. Let T : V → g be a linear map which is identified as an element in g ⊗ V ∗ ⊂ (g ⋉ρ∗ V ∗ ) ⊗ (g ⋉ρ∗ V ∗ ). Then r = T − T 21 is a skew-symmetric solution of CYBE in g ⋉ρ∗ V ∗ if and o ...
... Let g be a Lie algebra. Let ρ : g → gl(V ) be a representation of g and ρ∗ : g → gl(V ∗ ) be the dual representation. Let T : V → g be a linear map which is identified as an element in g ⊗ V ∗ ⊂ (g ⋉ρ∗ V ∗ ) ⊗ (g ⋉ρ∗ V ∗ ). Then r = T − T 21 is a skew-symmetric solution of CYBE in g ⋉ρ∗ V ∗ if and o ...
Hailperin`s Boole`s Algebra isn`t Boolean Algebra!
... (e.g., "human," "sheep") primarily as designating attributes rather than classes (i.e., thinking intensionally rather than extensionally). In this view the compound term "human sheep" has a wider, more inclusive, intension than either "human" or "sheep," whereas as a class it has a less inclusive ex ...
... (e.g., "human," "sheep") primarily as designating attributes rather than classes (i.e., thinking intensionally rather than extensionally). In this view the compound term "human sheep" has a wider, more inclusive, intension than either "human" or "sheep," whereas as a class it has a less inclusive ex ...
A primer of Hopf algebras
... success3 . Here Hopf algebras play a dual role: first the (left) invariant differential operators on an algebraic group form a cocommutative Hopf algebra, which coincides with the enveloping algebra of the Lie algebra in characteristic 0, but not in characteristic p. Second: the regular functions on ...
... success3 . Here Hopf algebras play a dual role: first the (left) invariant differential operators on an algebraic group form a cocommutative Hopf algebra, which coincides with the enveloping algebra of the Lie algebra in characteristic 0, but not in characteristic p. Second: the regular functions on ...
Conf
... “quotients”of the group G . So we have many information of the set in the acting group. Also the maximum expression of this fact is achieved if G is a Lie group or an algebraic group or a finite group and M is the space of a representation of G . Because the representations of simple Lie groups are ...
... “quotients”of the group G . So we have many information of the set in the acting group. Also the maximum expression of this fact is achieved if G is a Lie group or an algebraic group or a finite group and M is the space of a representation of G . Because the representations of simple Lie groups are ...
Contents Lattices and Quasialgebras Helena Albuquerque 5
... Faulkner and J.C. Ferrer [2] and renamed in [1] as null-symplectic triples. From two copies of a null-symplectic triple T we can get a 3-graded Lie algebra by declearing T as ±1-components and the inner derivation algebra of T as 0-component. In this way, any null-symplectic triple provides a (linea ...
... Faulkner and J.C. Ferrer [2] and renamed in [1] as null-symplectic triples. From two copies of a null-symplectic triple T we can get a 3-graded Lie algebra by declearing T as ±1-components and the inner derivation algebra of T as 0-component. In this way, any null-symplectic triple provides a (linea ...
[math.QA] 23 Feb 2004 Quantum groupoids and
... should satisfy certain functorial conditions, see [K]). When C is a category of H-modules, Z(C) is equivalent to the category of modules over the double DH. Definition 2.1. [DM1] Let C be a monoidal category and Z(C) its center. A commutative algebra in Z(C) is called a C-base algebra. When C is a c ...
... should satisfy certain functorial conditions, see [K]). When C is a category of H-modules, Z(C) is equivalent to the category of modules over the double DH. Definition 2.1. [DM1] Let C be a monoidal category and Z(C) its center. A commutative algebra in Z(C) is called a C-base algebra. When C is a c ...
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 ...
Topology Change for Fuzzy Physics: Fuzzy Spaces as Hopf Algebras
... Fuzzy spaces provide finite-dimensional approximations to certain symplectic manifolds M such as S 2 ≃ CP 1 , S 2 × S 2 and CP 2 . They are typically full matrix algebras M at(N + 1) of dimension (N + 1) × (N + 1). The fuzzy sphere SF2 (J) for angular momentum J = N2 for example is M at(N + 1). As N ...
... Fuzzy spaces provide finite-dimensional approximations to certain symplectic manifolds M such as S 2 ≃ CP 1 , S 2 × S 2 and CP 2 . They are typically full matrix algebras M at(N + 1) of dimension (N + 1) × (N + 1). The fuzzy sphere SF2 (J) for angular momentum J = N2 for example is M at(N + 1). As N ...
On the Associative Nijenhuis Relation
... the electronic journal of combinatorics 11 (2004), #R38 ...
... the electronic journal of combinatorics 11 (2004), #R38 ...