On the growth of graded polynomial identities of sl_n
Lucio Centrone, Manuela da Silva Souza
TL;DR
This paper investigates the growth of graded polynomial identities in G-graded Lie algebras, specifically calculating the exact Gelfand-Kirillov dimension for sl_n(K) with Z_n-grading.
Contribution
It provides the first explicit calculation of the Z_n-graded Gelfand-Kirillov dimension for sl_n(K) in the context of G-graded Lie PI-algebras.
Findings
Exact value of Z_n-graded Gelfand-Kirillov dimension for sl_n(K)
Introduction of the graded Gelfand-Kirillov dimension concept
Analysis of polynomial identity growth in graded Lie algebras
Abstract
Let K be a field of characteristic 0 and L be a G-graded Lie PI-algebra, where G is a finite group. We define the graded Gelfand-Kirillov dimension of L. Then we measure the growth of the Z_n-graded polynomial identities of the Lie algebra of n x n traceless matrices sl_n(K) giving an exact value of its Z_n-graded Gelfand-Kirillov dimension.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Rings, Modules, and Algebras