A Group-Theoretical Approach to the Periodic Table of
... and SO(3) ⊂ SO(4) ⊂ SO(4, 1) ⊂ SO(4, 2) ⊂ Sp(8, R) which are of relevance in the present work. 2.2 Representations of Lie groups and Lie algebras The concept of the representation of a group is essential for applications. A linear representation of dimension m of a group G is a homomorphic image of ...
... and SO(3) ⊂ SO(4) ⊂ SO(4, 1) ⊂ SO(4, 2) ⊂ Sp(8, R) which are of relevance in the present work. 2.2 Representations of Lie groups and Lie algebras The concept of the representation of a group is essential for applications. A linear representation of dimension m of a group G is a homomorphic image of ...
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... i.e. if ' holds under all interpretations over Kleene algebras with tests. We write KAT ' if ' holds under all interpretations over -continuous Kleene algebras with tests. ...
... i.e. if ' holds under all interpretations over Kleene algebras with tests. We write KAT ' if ' holds under all interpretations over -continuous Kleene algebras with tests. ...
A group-theoretical approach to the periodic table
... and SO(3) SO(4) SO(4, 1) SO(4, 2) Sp(8, R) which are of relevance in the present work. 2.2 Representations of Lie groups and Lie algebras The concept of the representation of a group is essential for applications. A linear representation of dimension m of a group G is a homomorphic image of ...
... and SO(3) SO(4) SO(4, 1) SO(4, 2) Sp(8, R) which are of relevance in the present work. 2.2 Representations of Lie groups and Lie algebras The concept of the representation of a group is essential for applications. A linear representation of dimension m of a group G is a homomorphic image of ...
full text (.pdf)
... The *-continuity condition says that < ~ * > X is the join or least upper bound of the propositionsX with
respect to implication. A proof that *-cant implies ind can be found in [K1]. The axiom *-cant appeared in
the original definition of dynamic algebras [K1], but later V. Pratt recommended ...
... The *-continuity condition says that < ~ * > X is the join or least upper bound of the propositions
cylindric algebras and algebras of substitutions^) 167
... 1.2.4 and 1.2.9], we have (ttI ) and (B). Finally, (jt3) holds by [6, 1.5.8(ii)], and (C) holds by L6, 1.5.7]. (ii) Let (A, +,-,-, ...
... 1.2.4 and 1.2.9], we have (ttI ) and (B). Finally, (jt3) holds by [6, 1.5.8(ii)], and (C) holds by L6, 1.5.7]. (ii) Let (A, +,-,-, ...
Leon Henkin and cylindric algebras. In
... The purely algebraic theory of cylindric algebras, exclusive of set algebras and representation theory, is fully developed in [71]. The parts of this theory due at mainly to Henkin are as follows. If A is a CAα and Γ = {ξ(0), . . . , ξ(m − 1)} is a finite subset of α, then we define c(Γ) a = cξ(0) · ...
... The purely algebraic theory of cylindric algebras, exclusive of set algebras and representation theory, is fully developed in [71]. The parts of this theory due at mainly to Henkin are as follows. If A is a CAα and Γ = {ξ(0), . . . , ξ(m − 1)} is a finite subset of α, then we define c(Γ) a = cξ(0) · ...
Free Field Approach to 2-Dimensional Conformal Field Theories
... product algebra of screening currents is nonlocal this is a nontrivial problem. In fact there exists a set of "basis contours" within which products of screenings obey the algebra of the positive root generators of the quantum group CfJ q(g ), q =exp(i7r/(k+hv)). It follows then quite easily that gi ...
... product algebra of screening currents is nonlocal this is a nontrivial problem. In fact there exists a set of "basis contours" within which products of screenings obey the algebra of the positive root generators of the quantum group CfJ q(g ), q =exp(i7r/(k+hv)). It follows then quite easily that gi ...
Exactly Solvable Problems in Quantum Mechanics
... solvability can be explained and derived in terms of hidden symmetry. However, even if it were true, it would probably not mean unifying all the ways to approach the problem. In fact, although many methods are based on symmetry, or – to be more specific – on the properties of Lie algebras, and altho ...
... solvability can be explained and derived in terms of hidden symmetry. However, even if it were true, it would probably not mean unifying all the ways to approach the problem. In fact, although many methods are based on symmetry, or – to be more specific – on the properties of Lie algebras, and altho ...
Converting Quadratic Relations To Factored Form
... have found the location of the vertex, it is possible to use its coordinates and the vertical stretch factor to rewrite the relation in vertex form. Both methods have their advantages and disadvantages, but should yield the same results. ...
... have found the location of the vertex, it is possible to use its coordinates and the vertical stretch factor to rewrite the relation in vertex form. Both methods have their advantages and disadvantages, but should yield the same results. ...
Composition algebras of degree two
... where n is a root of the equation 3^(1 — n) = 1 and 73 is the 3 by 3 identity matrix. The quadratic form w(x) = g trace(x2) allows composition for the new product *. A general definition of pseudo-octonions, valid over any field, can be found in [9]. Given 7 the algebraic closure of F, the forms of ...
... where n is a root of the equation 3^(1 — n) = 1 and 73 is the 3 by 3 identity matrix. The quadratic form w(x) = g trace(x2) allows composition for the new product *. A general definition of pseudo-octonions, valid over any field, can be found in [9]. Given 7 the algebraic closure of F, the forms of ...
A Quon Model
... In case a quon is a qudit of degree d, one has a simple representation for a 1-quon basis: the interior of a hemisphere contains two charged strings, each linking two of the output points. The value of the charge on one sting may equal either 0, 1, . . . , d − 1 ∈ Zd , while the other string carries ...
... In case a quon is a qudit of degree d, one has a simple representation for a 1-quon basis: the interior of a hemisphere contains two charged strings, each linking two of the output points. The value of the charge on one sting may equal either 0, 1, . . . , d − 1 ∈ Zd , while the other string carries ...
pdf-file. - Fakultät für Mathematik
... paths, and the s-condition. In 1984, Raymundo gave a survey lecture at the XVIIIth national congress of the Mexican Mathematical Society at Mérida [B10] under the title Incursions into the representation theory of algebras (in Spanish) about his own contributions as well as those of other Mexican m ...
... paths, and the s-condition. In 1984, Raymundo gave a survey lecture at the XVIIIth national congress of the Mexican Mathematical Society at Mérida [B10] under the title Incursions into the representation theory of algebras (in Spanish) about his own contributions as well as those of other Mexican m ...
Classical elliptic current algebras
... Green functions define the rLL-relations, the bialgebra structure and the analytic structure of half-currents. We do not write out explicitly the bialgebra structure related to the half-currents of the second classical elliptic algebra: it can be reconstructed along the lines of subsection 3.4. We d ...
... Green functions define the rLL-relations, the bialgebra structure and the analytic structure of half-currents. We do not write out explicitly the bialgebra structure related to the half-currents of the second classical elliptic algebra: it can be reconstructed along the lines of subsection 3.4. We d ...
Past Research
... I work on the cohomology, structure, and representations of various types of rings, such as Hopf algebras and group-graded algebras. My research program has involved collaborations with many mathematicians, including work with postdocs and graduate students. Below is a summary of some of my past res ...
... I work on the cohomology, structure, and representations of various types of rings, such as Hopf algebras and group-graded algebras. My research program has involved collaborations with many mathematicians, including work with postdocs and graduate students. Below is a summary of some of my past res ...
Tense Operators on Basic Algebras - Phoenix
... Let us note that if a basic algebra A is commutative then the assigned lattice L(A) is distributive (see [7], Theorem 8.5.9). The propositional logic corresponding to a commutative basic algebra was already described (see [3]). Our aim is to introduce tense operators G, H , F , P on any basic algebr ...
... Let us note that if a basic algebra A is commutative then the assigned lattice L(A) is distributive (see [7], Theorem 8.5.9). The propositional logic corresponding to a commutative basic algebra was already described (see [3]). Our aim is to introduce tense operators G, H , F , P on any basic algebr ...
INFINITESIMAL BIALGEBRAS, PRE
... The main results of this paper establish connections between infinitesimal bialgebras, pre-Lie algebras and dendriform algebras, which were a priori unexpected. An infinitesimal bialgebra (abbreviated ǫ-bialgebra) is a triple (A, µ, ∆) where (A, µ) is an associative algebra, (A, ∆) is a coassociativ ...
... The main results of this paper establish connections between infinitesimal bialgebras, pre-Lie algebras and dendriform algebras, which were a priori unexpected. An infinitesimal bialgebra (abbreviated ǫ-bialgebra) is a triple (A, µ, ∆) where (A, µ) is an associative algebra, (A, ∆) is a coassociativ ...
On the Structure of Abstract Algebras
... elements of ©, to be called the "proper domain" of/^ And, finally, let eachfi be a single-valued function of its proper domain to (£—in other words, let/^ assign to each sequence a of 2)^ a unique "/^-value" ft (a) in (J. Then the couple ((£, F) will be called an "abstract algebra" A, or for brevity ...
... elements of ©, to be called the "proper domain" of/^ And, finally, let eachfi be a single-valued function of its proper domain to (£—in other words, let/^ assign to each sequence a of 2)^ a unique "/^-value" ft (a) in (J. Then the couple ((£, F) will be called an "abstract algebra" A, or for brevity ...
On bimeasurings
... 1.1. Notation All vector spaces (algebras, coalgebras, bialgebras) will be over a ground field k. If A is an algebra and C a coalgebra, then Hom(C, A) denotes the convolution algebra of all linear maps from C to A. The unit and the multiplication on A are denoted by : k → A and m: A ⊗ A → A; the cou ...
... 1.1. Notation All vector spaces (algebras, coalgebras, bialgebras) will be over a ground field k. If A is an algebra and C a coalgebra, then Hom(C, A) denotes the convolution algebra of all linear maps from C to A. The unit and the multiplication on A are denoted by : k → A and m: A ⊗ A → A; the cou ...
Connections between relation algebras and cylindric algebras
... An n-dimensional cylindric basis of A is a set of n-dimensional networks over A, with certain closure properties. Each such basis forms the set of atoms of a finite n-dimensional cylindric algebra. If this is representable, so is A. • The set of all 3-dimensional networks is a 3-dimensional cylindri ...
... An n-dimensional cylindric basis of A is a set of n-dimensional networks over A, with certain closure properties. Each such basis forms the set of atoms of a finite n-dimensional cylindric algebra. If this is representable, so is A. • The set of all 3-dimensional networks is a 3-dimensional cylindri ...
L. Fortunato - INFN Padova
... • To them we can always associate an algebra that brings with itself a dynamical symmetry. • By knowing how to deal mathematically with the algebra one can get analytic solutions that can be compared with experimental data (not only: you can get also new, unexpected solutions!) • The algebra natural ...
... • To them we can always associate an algebra that brings with itself a dynamical symmetry. • By knowing how to deal mathematically with the algebra one can get analytic solutions that can be compared with experimental data (not only: you can get also new, unexpected solutions!) • The algebra natural ...