On star-homogeneous-graded polynomial identities of upper triangular matrices over an arbitrary field
Rings and Algebras
2024-02-06 v1
Abstract
We study the graded polynomial identities with a homogeneous involution on the algebra of upper triangular matrices endowed with a fine group grading. We compute their polynomial identities and a basis of the relatively free algebra, considering an arbitrary base field. We obtain the asymptotic behaviour of the codimension sequence when the characteristic of the base field is zero. As a consequence, we compute the exponent and the second exponent of the same algebra endowed with any group grading and any homogeneous involution.
Keywords
Cite
@article{arxiv.2402.02671,
title = {On star-homogeneous-graded polynomial identities of upper triangular matrices over an arbitrary field},
author = {Thiago Castilho de Mello and Felipe Yukihide Yasumura},
journal= {arXiv preprint arXiv:2402.02671},
year = {2024}
}