# A Frobenius-Schreier-Sims Algorithm to tensor decompose algebras

## TL;DR

This paper presents a novel tensor decomposition method for associative algebras, enabling efficient basis encoding and calculations for large algebras, inspired by the Schreier-Sims algorithm for permutation groups.

## Contribution

It introduces a Frobenius-Schreier-Sims inspired algorithm for tensor decomposition of associative algebras, extending computational capabilities.

## Key findings

- Enables basis encoding with logarithmic information
- Extends computational reach for large algebras
- Provides an algebraic analogue to Schreier-Sims algorithm

## Abstract

We introduce a decomposition of associative algebras into a tensor product of cyclic modules. This produces a means to encode a basis with logarithmic information and thus extends the reach of calculation with large algebras. Our technique is an analogue to the Schreier-Sims algorithm for permutation groups and is a by-product of Frobenius reciprocity.