Clifford algebras and their applications to Lie groups and spinors

Abstract

In these lectures, we discuss some well-known facts about Clifford algebras: matrix representations, Cartan's periodicity of 8, double coverings of orthogonal groups by spin groups, Dirac equation in different formalisms, spinors in $n$ dimensions, etc. We also present our point of view on some problems. Namely, we discuss the generalization of the Pauli theorem, the basic ideas of the method of averaging in Clifford algebras, the notion of quaternion type of Clifford algebra elements, the classification of Lie subalgebras of specific type in Clifford algebra, etc.

44 pages

References in corpus (2)

• Cambridge Lectures on Supersymmetry and Extra Dimensions
• Constant solutions of Yang-Mills equations and generalized Proca equations

Cited by in corpus (8)

• On inner automorphisms preserving subspaces of Clifford algebras
• On generalization of Lipschitz groups and spin groups
• Basis-free solution to Sylvester equation in Clifford algebra of arbitrary dimension
• On SVD and Polar Decomposition in Real and Complexified Clifford Algebras
• A Note on Centralizers and Twisted Centralizers in Clifford Algebras
• On Rank of Multivectors in Geometric Algebras
• Generalized Degenerate Clifford and Lipschitz Groups in Geometric Algebras
• On Lie Groups Preserving Subspaces of Degenerate Clifford Algebras