The preprojective algebra of a finite EI quiver

TL;DR

This paper introduces the preprojective algebra for finite EI quivers, showing its isomorphism to a tensor algebra and, in Cartan type cases, to a generalized preprojective algebra, expanding algebraic understanding.

Contribution

It defines the preprojective algebra for finite EI quivers and establishes its isomorphism to tensor and generalized preprojective algebras in specific cases.

Findings

Preprojective algebra is isomorphic to a tensor algebra.

In Cartan type, it is isomorphic to a generalized preprojective algebra.

Provides a new algebraic framework for finite EI quivers.

Abstract

We define the preprojective algebra of a finite EI quiver. We prove that it is isomorphic to a centain tensor algebra. For a finite EI quiver of Cartan type, we prove that the corresponding preprojective algebra is isomorphic to the generalized preprojective algebra.