Convolution algebra of diagram automorphism fixed quiver variety

TL;DR

This paper investigates the convolution algebra structure of fixed point quiver varieties under diagram automorphisms and establishes a homomorphism from a universal enveloping algebra to this convolution algebra.

Contribution

It introduces a new algebraic framework connecting fixed point quiver varieties with universal enveloping algebras of automorphism fixed algebras.

Findings

Existence of an algebra homomorphism from the universal enveloping algebra to the convolution algebra.

Identification of the convolution algebra structure on fixed point quiver varieties.

Extension of algebraic structures to diagram automorphism fixed points.

Abstract

We study the convolution algebra $H_{*}(Z^{\theta}_{W})$ of homology on diagram automorphism fixed point quiver variety and prove that there exists an algebra homomorphism from the universal enveloping algebra of the diagram automorphism fixed algebra of the split quiver to $H_{*}(Z^{\theta}_{W})$.