Classification of extended Clifford algebras

TL;DR

This paper classifies extended Clifford algebras formed from tensor products of commutative and real Clifford algebras, identifying five types and demonstrating their closure under tensor product operations.

Contribution

It introduces a classification of extended Clifford algebras into five types and proves their closure properties under tensor products.

Findings

Five types of extended Clifford algebras identified

Extended Clifford algebras are closed under tensor product

Provides a structural framework for these algebras

Abstract

Considering tensor products of special commutative algebras and general real Clifford algebras, we arrive at extended Clifford algebras. We have found that there are five types of extended Clifford algebras. The class of extended Clifford algebras is closed with respect to the tensor product.