Determinants of finite-dimensional algebras

TL;DR

This paper introduces a canonical determinant function for finite-dimensional associative algebras over a normal base, exploring its properties and applications to the topology of the moduli stack of such algebras.

Contribution

It defines a new determinant construction for finite-dimensional algebras and investigates its properties and topological applications.

Findings

The determinant function has specific algebraic properties.

Applications to the topology of the moduli stack are demonstrated.

The construction provides new insights into algebra classification.

Abstract

To each associative unitary finite-dimensional algebra over a normal base, we associative a canonical multiplicative function called its determinant. We give various properties of this construction, as well as applications to the topology of the moduli stack of n-dimensional algebras.