On Suslin Matrices and their connection to Spin groups

TL;DR

This paper presents an explicit construction of Clifford algebras using Suslin matrices, analyzing their connection to Spin groups and providing insights into their algebraic properties and low-dimensional computations.

Contribution

It introduces a concrete representation of Clifford algebras via Suslin matrices, linking them to Spin groups and offering a new perspective on their properties.

Findings

Explicit Suslin matrix representation of Clifford algebras

Analysis of Spin groups and involutions using this representation

Insights into low-dimensional algebraic computations

Abstract

A concrete representation of the Clifford algebra (for any hyperbolic quadratic space) is given using what are called Suslin matrices. This explicit construction is used to analyze the corresponding Spin groups and the involution and might be of interest in low dimensional computations. Conversely, this connection to Clifford algebras gives a conceptual foundation to some (seemingly accidental) properties of Suslin matrices.