Cocharacters and gradedGelfandKirillov dimension for PIalgebras
Full text  
Author(s): 
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. 11251140, SEP 2016. 
Web of Science Citations:  0 
Abstract  
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 TGideal of Ggraded identities of a Ggraded algebra in characteristic 0 and the generators of the TGxZ2 ideal of G x Z(2)graded identities of its tensor product by the infinitedimensional 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 Ek{*} circle times E over an infinite field of characteristic p > 2, where Ek{*} 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 Ek{*} is p if p > k. Moreover, we find a basis of the Z(2) x Z(2)graded identities of Ek ({*}) 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 GelfandKirillov (GK) dimension of Ek{*} circle times E. (AU)  
FAPESP's process:  15/089615  Growth of algebras with polynomial identities 
Grantee:  Lucio Centrone 
Support type:  Regular Research Grants 
FAPESP's process:  13/067524  Cocharacters and gradedGelfandKirillov dimension for PIalgebras 
Grantee:  Lucio Centrone 
Support type:  Regular Research Grants 