Symplectic, orthogonal and linear Lie groups in Clifford algebra

TL;DR

This paper establishes isomorphisms between certain Lie groups within Clifford algebra and classical matrix Lie groups, along with their Lie algebras, for arbitrary dimensions and fixed signatures.

Contribution

It provides new mathematical isomorphisms linking Clifford algebra Lie groups to classical matrix Lie groups and their Lie algebras, extending to arbitrary dimensions.

Findings

Isomorphisms between 5 Lie groups in Clifford algebra and classical matrix Lie groups.

Corresponding Lie algebra isomorphisms.

Applicable to groups of arbitrary dimension and fixed signatures.

Abstract

In this paper we prove isomorphisms between 5 Lie groups (of arbitrary dimension and fixed signatures) in Clifford algebra and classical matrix Lie groups - symplectic, orthogonal and linear groups. Also we obtain isomorphisms of corresponding Lie algebras.