Martindale algebras of quotients of graded algebras
Hannes Bierwirth, Candido Martin Gonzalez, Juana Sanchez Ortega, and Mercedes Siles Molina
TL;DR
This paper explores the relationship between maximal graded algebras of quotients and their zero components in Lie and associative algebras, applying findings to finitary complex Lie algebras.
Contribution
It establishes connections between graded quotients and their zero components, and computes maximal quotients for finitary complex Lie algebras.
Findings
Zero component of maximal graded algebra of quotients relates to the maximal quotient of the zero component.
Finitary complex Lie algebras are strongly nondegenerate.
Maximal algebras of quotients for these Lie algebras are explicitly computed.
Abstract
The motivation for this paper has been to study the relation between the zero component of the maximal graded algebra of quotients and the maximal graded algebra of quotients of the zero component, both in the Lie case and when considering Martindale algebras of quotients in the associative setting. We apply our results to prove that the finitary complex Lie algebras are (graded) strongly nondegenerate and compute their maximal algebras of quotients.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Finite Group Theory Research