Group Gradings on Simple Lie Algebras of Type "A"
Y. A. Bahturin, M. V. Zaicev
TL;DR
This paper classifies all possible group gradings by finite abelian groups on simple Lie algebras of type "A" over algebraically closed fields of characteristic zero, providing a comprehensive understanding of their structure.
Contribution
It offers a complete description of all group gradings on type "A" simple Lie algebras, a previously unresolved classification problem.
Findings
All gradings by finite abelian groups are classified.
Explicit descriptions of each grading are provided.
The results apply to all simple Lie algebras of type "A" over algebraically closed fields.
Abstract
In this paper we describe all group gradings by a finite abelian group G of any Lie algebra L of the type "A" over algebraically closed field F of characteristic zero.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Algebra and Geometry