Tilting, deformations and representations of linear groups over Euclidean algebras

TL;DR

This paper studies the dual space of linear groups over Euclidean algebras, revealing a dense subset isomorphic to products of dual spaces of linear groups, using bimodule categories and quiver representations.

Contribution

It characterizes the structure of the dual space over Euclidean algebras, showing it contains a dense open subset with a specific product structure.

Findings

Identifies a dense open subset in the dual space isomorphic to a product of dual spaces.

Uses bimodule categories and quiver representations for the analysis.

Provides explicit descriptions of the additional space involved.

Abstract

We consider the dual space of linear groups over Dynkinian and Euclidean algebras, i.e. finite dimensional algebras derived equivalent to the path algebra of Dynkin or Euclidean quiver. We prove that this space contains an open dense subset isomorphic to the product of dual spaces of full linear groups and, perhaps, one more (explicitly described) space. The proof uses the technique of bimodule categories, deformations and representations of quivers.