Quantum generalized Kac--Moody algebras via Hall algebras of complexes

arXiv1906.12246MaRDI QIDQ6321222

Jonathan D. Axtell, Kyu-Hwan Lee

Publication date: 28 June 2019

Abstract: We establish an embedding of the quantum enveloping algebra of a symmetric generalized Kac--Moody algebra into a localized Hall algebra of $mathbb{Z}_2$-graded complexes of representations of a quiver with (possible) loops. To overcome difficulties resulting from the existence of infinite dimensional projective objects, we consider the category of finitely-presented representations and the category of $mathbb{Z}_2$-graded complexes of projectives with finite homology.

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