Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/323458
Type: Artigo
Title: The G-graded Identities Of The Grassmann Algebra
The G-graded identities of the Grassmann algebra
Author: Centrone, Lucio
Abstract: Let G be a finite abelian group with identity element 1G and (Formula present) be an infinite dimensional G-homogeneous vector space over a field of characteristic 0. Let E = E(L) be the Grassmann algebra generated by L. It follows that E is a G-graded algebra. Let |G| be odd, then we prove that in order to describe any ideal of G-graded identities of E it is sufficient to deal with G′-grading, where |G′| ≤ |G|, dimF L1G′ = ∞ and dimF Lg′ < ∞ if g′ = 1G′. In the same spirit of the case |G| odd, if |G| is even it is sufficient to study only those G-gradings such that dimF Lg = ∞, where o(g) = 2, and all the other components are finite dimensional. We also compute graded cocharacters and codimensions of E in the case dim (Formula present) and dim (Formula present) if g ≠ 1G. © 2016, Masarykova Universita. All rights reserved.
Let G be a finite abelian group with identity element 1G and L = L g∈G Lg be an infinite dimensional G-homogeneous vector space over a field of characteristic 0. Let E = E(L) be the Grassmann algebra generated by L. It follows that E is a G-graded algebra
Subject: Graded Polynomial Identities
Álgebras graduadas
Identidades polinomiais graduadas
Co-caracter
Grassmann, Álgebra de
Country: República Checa
Editor: Masarykova Univerzita
Citation: Archivum Mathematicum. Masarykova Universita, v. 52, n. 3, p. 141 - 158, 2016.
Rights: fechado
fechado
Identifier DOI: 10.5817/AM2016-3-141
Address: https://dml.cz/handle/10338.dmlcz/145829
Date Issue: 2016
Appears in Collections:IMECC - Artigos e Outros Documentos

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