Tame quivers and affine enveloping algebras
Yong Jiang, Jie Sheng

TL;DR
This paper constructs integral bases for the positive part of affine Kac-Moody algebras' enveloping algebra using Hall algebra techniques, leveraging tame quiver representation theory.
Contribution
It introduces a novel Hall algebra approach to explicitly construct integral bases for the enveloping algebra of affine Kac-Moody algebras, connecting quiver representations with algebraic structures.
Findings
Explicit integral bases for $U( ^+)$ constructed
Hall algebra approach effectively applied to affine Kac-Moody algebras
Representation theory of tame quivers is central to the construction
Abstract
Let be an affine Kac-Moody algebra with symmetric Cartan datum, be the maximal nilpotent subalgebra of . By the Hall algebra approach, we construct integral bases of the -form of the enveloping algebra . In particular, the representation theory of tame quivers is essentially used in this paper.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Topics in Algebra
