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

Autor(es)

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

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Linear Algebra and its Applications; v. 471, p. 469-499, APR 15 2015.
• Citações Web of Science: 1

Resumo

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)

• Processo FAPESP: 13/06752-4 - Cocaracteres e dimenção de Gelfand-Kirillov de PI-álgebras
• Beneficiário: Lucio Centrone
• Modalidade de apoio: Auxílio à Pesquisa - Regular