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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

THE G-GRADED IDENTITIES OF THE GRASSMANN ALGEBRA

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Author(s):
Centrone, Lucid
Total Authors: 1
Document type: Journal article
Source: ARCHIVUM MATHEMATICUM; v. 52, n. 3, p. 141-158, 2016.
Web of Science Citations: 0
Abstract

Let G be a finite abelian group with identity element 1(G) and L = (g is an element of G) L-g 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 broken vertical bar G'broken vertical bar dim(F) L(1)G' = Do and dimF L-g = infinity 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 dim(F) L-g = infinity, 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 L(1)G Do and dim L9 < Do if g not equal 1(G). (AU)

FAPESP's process: 15/08961-5 - Growth of algebras with polynomial identities
Grantee:Lucio Centrone
Support type: Regular Research Grants
FAPESP's process: 13/06752-4 - Cocharacters and gradedGelfand-Kirillov dimension for PI-algebras
Grantee:Lucio Centrone
Support type: Regular Research Grants