On star-homogeneous-graded polynomial identities of upper triangular matrices over an arbitrary field

2024/02/05 by de Mello, Thiago Castilho, Yasumura, Felipe Yukihide · 1 citation
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2402.02671

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.

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• Graded algebras with homogeneous involution and varieties of almost polynomial growth

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