Graded polynomial identities for the Lie algebra of upper triangular matrices of order 3
Felipe Yukihide Yasumura
TL;DR
This paper computes the graded polynomial identities and codimension sequence for elementary gradings of the Lie algebra of 3x3 upper triangular matrices, advancing understanding of their algebraic structure.
Contribution
It provides the first explicit computation of graded identities and codimensions for these specific Lie algebras with elementary gradings.
Findings
Explicit graded identities are derived for the algebra.
The graded codimension sequence is characterized.
Results contribute to the classification of polynomial identities in Lie algebras.
Abstract
We compute the graded polynomial identities and its graded codimension sequence for the elementary gradings of the Lie algebra of upper triangular matrices of order 3.
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Taxonomy
TopicsAdvanced Topics in Algebra · Nonlinear Waves and Solitons · Advanced Differential Equations and Dynamical Systems