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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.)

A note on graded polynomial identities for tensor products by the Grassmann algebra in positive characteristic

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Centrone, Lucio ; Tomaz da Silva, Viviane Ribeiro
Total Authors: 2
Document type: Journal article
Source: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION; v. 26, n. 6, p. 1125-1140, SEP 2016.
Web of Science Citations: 0

Let G be a finite abelian group. As a consequence of the results of Di Vincenzo and Nardozza, we have that the generators of the T-G-ideal of G-graded identities of a G-graded algebra in characteristic 0 and the generators of the T-GxZ2 -ideal of G x Z(2)-graded identities of its tensor product by the infinite-dimensional Grassmann algebra E endowed with the canonical grading have pairly the same degree. In this paper, we deal with Z(2) x Z(2)-graded identities of E-k{*} circle times E over an infinite field of characteristic p > 2, where E-k{*} is E endowed with a specific Z(2)-grading. We find identities of degree p + 1 and p + 2 while the maximal degree of a generator of the Z(2)-graded identities of E-k{*} is p if p > k. Moreover, we find a basis of the Z(2) x Z(2)-graded identities of E-k ({*}) circle times E and also a basis of multihomogeneous polynomials for the relatively free algebra. Finally, we compute the Z(2) x Z(2)-graded Gelfand-Kirillov (GK) dimension of E-k{*} circle times E. (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