Search results for "Filtered algebra"

The Representation Type of the Centre of a Group Algebra

1986

Quantum and Braided Integrals

2001

We give a pedagogical introduction to integration techniques appropriate for non-commutative spaces while presenting some new results as well. A rather detailed discussion outlines the motivation for adopting the Hopf algebra language. We then present some trace formulas for the integral on Hopf algebras and show how to treat the $\int 1=0$ case. We extend the discussion to braided Hopf algebras relying on diagrammatic techniques. The use of the general formulas is illustrated by explicitly worked out examples.

On the graded identities and cocharacters of the algebra of 3×3 matrices

2004

Abstract Let M2,1(F) be the algebra of 3×3 matrices over an algebraically closed field F of characteristic zero with non-trivial Z 2 -grading. We study the graded identities of this algebra through the representation theory of the hyperoctahedral group Z 2 ∼S n . After splitting the space of multilinear polynomial identities into the sum of irreducibles under the Z 2 ∼S n -action, we determine all the irreducible Z 2 ∼S n -characters appearing in this decomposition with non-zero multiplicity. We then apply this result in order to study the graded cocharacter of the Grassmann envelope of M2,1(F). Finally, using the representation theory of the general linear group, we determine all the grade…

The γ5-problem and anomalies — A Clifford algebra approach

1990

Abstract It is shown that a strong correspondence between noncyclicity and anomalies exists. This allows, by fundamental properties of Clifford algebras, to build a simple and consistent scheme for treating γ 5 without using ( d −4)-dimensional objects

NONCOMMUTATIVE GEOMETRY AND GRADED ALGEBRAS IN ELECTROWEAK INTERACTIONS

1992

The Standard Model of Electroweak Interactions can be described by a generalized Yang-Mills field incorporating both the usual gauge bosons and the Higgs fields. The graded derivative by means of which the Yang-Mills field strength is constructed involves both a differential acting on space-time and a differential acting on an associative graded algebra of matrices. The square of the curvature for the corresponding covariant derivative yields the bosonic Lagrangian of the Standard Model. We show how to recover the whole fermionic part of the Standard Model in this framework. Quarks and leptons fit naturally into the smallest typical and nontypical irreducible representations of the graded …

GRADED IDENTITIES FOR THE ALGEBRA OF n×n UPPER TRIANGULAR MATRICES OVER AN INFINITE FIELD

2003

We consider the algebra Un(K) of n×n upper triangular matrices over an infinite field K equipped with its usual ℤn-grading. We describe a basis of the ideal of the graded polynomial identities for this algebra.

Cocharacters of group graded algebras and multiplicities bounded by one

2017

Let G be a finite group and A a G-graded algebra over a field F of characteristic zero. We characterize the (Formula presented.)-ideals (Formula presented.) of graded identities of A such that the multiplicities (Formula presented.) in the graded cocharacter of A are bounded by one. We do so by exhibiting a set of identities of the (Formula presented.)-ideal. As a consequence we characterize the varieties of G-graded algebras whose lattice of subvarieties is distributive.

An Operator Theoretical Approach to Enveloping ϕ* - and C* - Algebras of Melrose Algebras of Totally Characteristic Pseudodifferential Operators

1998

Let X be a compact manifold with boundary. It will be shown (Theorem 3.4) that the small Melrose algebra A≔ ϕb,cl (χ,bΩ1/2) (cf. [22], [23]) of classical, totally characteristic pseudodifferential operators carries no topology such that it is a topological algebra with an open group of invertible elements, in particular, the algebra A cannot be spectrally invariant in any C* – algebra. On the other hand, the symbolic structure of A can be extended continuously to the C* – algebra B generated by A as a subalgebra of ζ(σbL2(χ, bΩ1/2)) by a generalization of a method of Gohberg and Krupnik. Furthermore, A is densely embedded in a Frechet algebra A ⊆ B which is a ϕ* – algebra in the sense of Gr…

On the projectives of a group algebra

1980

Hom-Lie quadratic and Pinczon Algebras

2017

ABSTRACTPresenting the structure equation of a hom-Lie algebra 𝔤, as the vanishing of the self commutator of a coderivation of some associative comultiplication, we define up to homotopy hom-Lie algebras, which yields the general hom-Lie algebra cohomology with value in a module. If the hom-Lie algebra is quadratic, using the Pinczon bracket on skew symmetric multilinear forms on 𝔤, we express this theory in the space of forms. If the hom-Lie algebra is symmetric, it is possible to associate to each module a quadratic hom-Lie algebra and describe the cohomology with value in the module.