Quivers with relations for symmetrizable Cartan matrices II : Convolution algebras
Christof Geiss, Bernard Leclerc, Jan Schr\"oer
TL;DR
This paper constructs a convolution algebra of constructible functions on module varieties of specific Iwanaga-Gorenstein algebras to realize the positive part of symmetrizable Kac-Moody algebra's enveloping algebra.
Contribution
It introduces a novel realization of the enveloping algebra using convolution algebras associated with Iwanaga-Gorenstein algebras.
Findings
Realization of the enveloping algebra as a convolution algebra
Connection between module varieties and Kac-Moody algebra structure
New algebraic framework for symmetrizable Cartan matrices
Abstract
We realize the enveloping algebra of the positive part of a symmetrizable Kac-Moody algebra as a convolution algebra of constructible functions on module varieties of some Iwanaga-Gorenstein algebras of dimension 1.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry