Fast matrix representation for Clifford algebras

TL;DR

This paper introduces two efficient algorithms for matrix representation of Clifford algebras, leveraging recursive decomposition, with implementations in Rust available as open-source tools.

Contribution

The paper presents novel recursive algorithms for Clifford algebra matrix representations and analyzes their relations and automorphisms.

Findings

Algorithms are faster due to recursive decomposition

Explicit forms of automorphisms are derived

Rust implementation available as open-source

Abstract

In this paper, we present two fast matrix representation algorithms based on the recursive decomposition of multivectors into specific right and left ideals. We also examine the relation between these two representations. Furthermore, we derive the explicit forms of the fundamental (anti)automorphisms of these Clifford algebra representations, and the efficient methods to compute them. The algorithms have been implemented in Rust and are available as the Cargo crate clifft on Github, released under the MIT license.