Development of the method of quaternion typification of Clifford algebra elements

Abstract

In this paper we further develop the method of quaternion typification of Clifford algebra elements suggested by the author in the previous paper. On the basis of new classification of Clifford algebra elements it is possible to reveal and prove a number of new properties of Clifford algebra. We use k-fold commutators and anticommutators. In this paper we consider Clifford and exterior degrees and elementary functions of Clifford algebra elements.

15 pages

References in corpus (3)

• Unitary spaces on Clifford algebras
• Quaternion typification of Clifford algebra elements
• A classification of Lie algebras of pseudounitary groups in the techniques of Clifford algebras

Cited by in corpus (11)

• 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
• 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
• Basis-free Formulas for Characteristic Polynomial Coefficients in Geometric Algebras
• A Note on Centralizers and Twisted Centralizers in Clifford Algebras
• Generalized Degenerate Clifford and Lipschitz Groups in Geometric Algebras
• On Lie Groups Preserving Subspaces of Degenerate Clifford Algebras