Quantum Chevalley groups

TL;DR

This paper constructs quantum analogues of Chevalley groups within quantum group completions, deriving identities that generalize classical results and connect to quantum dilogarithm identities, advancing the understanding of quantum algebraic structures.

Contribution

It introduces quantum Chevalley groups inside Hall algebra completions and derives identities that extend classical and quantum dilogarithm relations.

Findings

Derived pentagonal identities in quantum Chevalley groups

Connected quantum identities to Faddeev-Volkov quantum dilogarithms

Extended classical identities to quantum algebra context

Abstract

The goal of this paper is to construct quantum analogues of Chevalley groups inside completions of quantum groups or, more precisely, inside completions of Hall algebras of finitary categories. In particular, we obtain pentagonal and other identities in the quantum Chevalley groups which generalize their classical counterparts and explain Faddeev-Volkov quantum dilogarithmic identities and their recent generalizations due to Keller