A geometric construction of $U(\mathfrak{n})$ for affine Kac-Moody algebras of type $\tilde{\mathsf{C}}_{n}$

Abstract

Inspired by the work of Geiss, Leclerc and Schr\"oer [Represent. Theory 20, (2016)] we realize the enveloping algebra of the positive part of an affine Kac-Moody Lie algebra of Dynkin type $\tilde{\mathsf{C}}_n$ as a generalized composition algebra of constructible functions on the varieties of locally free representations of the corresponding 1-Iwanaga-Gorenstein algebra $H=H_{\mathbb{C}}(C,D,\Omega)$ with minimal symmetrizer $D$ and arbitrary orientation $\Omega$. To this end, we exploit in several ways the fact that in this situation $H$ is a string algebra.