Testing isomorphism of graded algebras

TL;DR

This paper introduces a new polynomial-time algorithm for testing isomorphism of finite graded algebras, especially effective for nilpotent Lie algebras, with practical heuristics and implementation details.

Contribution

The paper presents a novel algorithm for algebra isomorphism testing with proven polynomial complexity for a broad class of nilpotent Lie algebras.

Findings

Algorithm runs in polynomial time for a broad class of nilpotent Lie algebras.

Heuristics significantly improve practical performance.

Implementation in Magma demonstrates effectiveness.

Abstract

We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that often dramatically improve the performance of the algorithm and report on an implementation in Magma.