Graded polynomial identities and Specht property for the Lie algebra of upper triangular matrices of order 3

2024/12/17 by Daniela Martinez Correa, Felipe Yukihide Yasumura, Correa, Daniela Martinez +1
Mathematics · Medicine · Computer Science · #Advanced Topics in Algebra #Phytoestrogen effects and research #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2412.13325

Abstract

We compute the graded polynomial identities for the variety of graded algebras generated by the Lie algebra of upper triangular matrices of order 3 over an arbitrary field and endowed with an elementary grading. We investigate the Specht property for the same family of varieties.

Related

• Specht property of varieties of graded Lie algebras
• Graded polynomial identities of the infinite-dimensional upper triangular matrices over an arbitrary field
• On star-homogeneous-graded polynomial identities of upper triangular matrices over an arbitrary field
• Gradings on the algebra of triangular matrices as a Lie algebra: revisited
• Gradings, graded identities, *-identities and graded *-identities of an algebra of upper triangular matrices