Quaternion typification of Clifford algebra elements

Abstract

We present a new classification of Clifford algebra elements. Our classification is based on the notion of quaternion type. Using this classification we develop a method for analyzing of commutators and anticommutators of Clifford algebra elements. This method allows us to find out and prove a number of new properties of Clifford algebra elements.

14 pages

References in corpus (2)

• Unitary spaces on Clifford algebras
• A classification of Lie algebras of pseudounitary groups in the techniques of Clifford algebras

Cited by in corpus (16)

• On computing the determinant, other characteristic polynomial coefficients, and inverse in Clifford algebras of arbitrary dimension
• Clifford algebras and their applications to Lie groups and spinors
• Development of the method of quaternion typification of Clifford algebra elements
• Classification of Lie algebras of specific type in complexified Clifford algebras
• On some Lie groups containing spin group in Clifford algebra
• Symplectic, orthogonal and linear Lie groups in Clifford algebra
• On generalization of Lipschitz groups and spin groups
• On inner automorphisms preserving subspaces of Clifford algebras
• Method of averaging in Clifford algebras
• Basis-free Formulas for Characteristic Polynomial Coefficients in Geometric Algebras
• A Note on Centralizers and Twisted Centralizers in Clifford Algebras
• Compositions of invertibility preserving maps for some monoids and their application to Clifford algebras
• Application of the method of quaternion typification for finding subalgebras and Lie subalgebras of Clifford algebras
• Development of the Method of Averaging in Clifford Geometric Algebras
• Generalized Degenerate Clifford and Lipschitz Groups in Geometric Algebras
• On Lie Groups Preserving Subspaces of Degenerate Clifford Algebras