Gradings on simple algebras of finitary matrices
Yuri Bahturin, Mikhail Zaicev
TL;DR
This paper classifies gradings by finite abelian groups on algebras of infinite matrices with finitely many nonzero entries over an algebraically closed field of characteristic zero.
Contribution
It provides a complete description of gradings on simple algebras of finitary matrices, extending the understanding of algebraic gradings to infinite-dimensional cases.
Findings
Classified all gradings by finite abelian groups on these algebras.
Extended finite-dimensional grading results to infinite matrices.
Clarified structure of automorphisms related to gradings.
Abstract
We describe gradings by finite abelian groups on the associative algebras of infinite matrices with finitely many nonzero entries, over an algebraically closed field of characteristic zero.
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Taxonomy
TopicsAdvanced Topics in Algebra · Matrix Theory and Algorithms · Algebraic structures and combinatorial models