On Z(2)-graded identities of UT2(E) and their growth

Author(s)

Centrone, Lucio ^[1] ; Tomaz da Silva, Viviane Ribeiro ^[2]

Affiliation

^[1] Univ Estadual Campinas, IMECC, BR-13083859 Campinas, SP - Brazil

^[2] Univ Fed Minas Gerais, Inst Ciencias Exatas, Dept Matemat, BR-31270901 Belo Horizonte, MG - Brazil

• Document type: Journal article
• Source: Linear Algebra and its Applications; v. 471, p. 469-499, APR 15 2015.
• Web of Science Citations: 1

Abstract

Let F be an infinite field of characteristic different from two and E be the infinite dimensional Grassmann algebra over F. We consider the upper triangular matrix algebra UT2(E) with entries in E endowed with the Z(2)-grading inherited by the natural Z(2)-grading of E and we study its ideal of Z(2)-graded polynomial identities (T-Z2-ideal) and its relatively free algebra. In particular we show that the set of Z(2)-graded polynomial identities of UT2(E) does not depend on the characteristic of the field. Moreover we compute the Z(2)-graded Hilbert series of UT2(E) and its Z(2)-graded Gelfand-Kirillov dimension. (C) 2015 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 13/06752-4 - Cocharacters and gradedGelfand-Kirillov dimension for PI-algebras
• Grantee: Lucio Centrone
• Support Opportunities: Regular Research Grants