Crystal bases, dilogarithm identities and torsion in algebraic K-groups

TL;DR

This paper offers a new interpretation and proof of dilogarithm identities linked to affine Kac-Moody algebra sl(2)^, utilizing crystal basis path descriptions and exploring their connections to algebraic K-theory.

Contribution

It introduces a novel proof of dilogarithm identities via crystal bases and discusses their relation to algebraic K-theory, providing new insights into these mathematical structures.

Findings

New proof of dilogarithm identities using crystal basis paths

Connections established between dilogarithm identities and algebraic K-theory

Enhanced understanding of the structure of affine Kac-Moody algebra sl(2)^

Abstract

We give a new interpretation and proof of the dilogarithm identities, associated to the affine Kac-Moody algebra sl(2)^, using the path description of the corresponding crystal basis. We also discuss connections with algebraic K-theory.