Characterizing Nilpotent Associative Algebras by Their Multiplier

TL;DR

This paper studies a measure related to the Schur multiplier in associative algebras, characterizing all finite-dimensional nilpotent associative algebras with this measure being ten or less, using Lie theory techniques.

Contribution

It introduces a novel measure for associative algebras and provides a complete classification of nilpotent algebras with small measure values.

Findings

Characterization of nilpotent associative algebras with measure ≤10

Application of Lie theory methods to associative algebra classification

Complete classification results for specific measure bounds

Abstract

The paper concerns an analogue of the famous Schur multiplier in the context of associative algebras and a measure of how far its dimension is from being maximal. Applying a methodology from Lie theory, we characterize all finite-dimensional nilpotent associative algebras for which this measure is ten or less.