Quaternion types of Clifford algebra elements, basis-free approach

2011/09/11 by Dmitry Shirokov, Shirokov, D. S.
Mathematics · #Algebraic and Geometric Analysis #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1109.2322

openalex publication_date 2011/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider Clifford algebras over the field of real or complex numbers as a quotient algebra without fixed basis. We present classification of Clifford algebra elements based on the notion of quaternion type. This classification allows us to reveal and prove a number of new properties of Clifford algebras. We rely on the operations of conjugation to introduce the notion of quaternion type. Also we find relations between the concepts of quaternion type and rank of Clifford algebra element.

Related

• Application of the method of quaternion typification for finding subalgebras and Lie subalgebras of Clifford algebras
• Characterizing quaternion rings over an arbitrary base
• Clifford Type Algebra Characteristics Investigation
• A Clifford algebra associated to generalized Fibonacci quaternions
• Expository paper on Clifford algebras ,representations , and the octonion algebra