Gradings on the algebra of triangular matrices as a Lie algebra: revisited

2021/03/22 by Koshlukov, Plamen, Yasumura, Felipe Yukihide
#16R99 #16W50 #17B30 #FOS: Mathematics #Primary: 17B70 #Rings and Algebras (math.RA) #Secondary: 17B01

paper · doi:10.48550/arxiv.2103.11977

Abstract

We investigate the group gradings on the algebra of upper triangular matrices over an arbitrary field, viewed as a Lie algebra. These results were obtained a few years early by the same authors. We provide streamlined proofs, and present a complete classification of isomorphism classes of the gradings. We also provide a classification of the practical isomorphism classes of the gradings, which is a better alternative way to consider these gradings up to being essentially the same object. Finally, we investigate in details the case where the characteristic of the base field is 2, a topic that was neglected in previous works.

Related

• On the graded automorphisms of upper triangular matrix algebras
• Graded Identities and Isomorphisms on Algebras of Upper Block-Triangular\n Matrices
• On the Number of Gradings on Matrix Algebras
• Graded polynomial identities and Specht property for the Lie algebra of upper triangular matrices of order 3
• Group gradings on triangularizable algebras