Fundamental Automorphisms of Clifford Algebras and an Extension of Dabrowski Pin Groups

Abstract

Double coverings of the orthogonal groups of the real and complex spaces are considered. The relation between discrete transformations of these spaces and fundamental automorphisms of Clifford algebras is established, where an isomorphism between a finite group of the discrete transformations and an automorphism group of the Clifford algebras plays a central role. The complete classification of Dabrowski groups depending upon signatures of the spaces is given. Two types of Dabrowski quotient groups are introduced in case of odd-dimensional spaces. Application potentialities of the introduced quotient groups in Physics are discussed.

arXiv comment30 pages, LaTeX2e, corrected version

References in corpus (6)

• About Zitterbewegung and electron structure
• Dirac-Hestenes spinor fields in Riemann-Cartan spacetime
• Some applications of differential topology in general relativity
• On the Obstructions to non-Cliffordian Pin Structures
• Spin Structures on Kleinian Manifolds
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Cited by in corpus (8)

• CPT groups of higher spin fields
• Hyperspherical Functions and Linear Representations of the Lorentz Group
• Group Theoretical Interpretation of the CPT-theorem
• The CPT Group in the de Sitter Space
• A Note on the Majorana-Oppenheimer Quantum Electrodynamics
• Spinor Representations of Surfaces in 4-Dimensional Pseudo-Riemannian Manifolds
• Hyperspherical Functions and Harmonic Analysis on the Lorentz Group
• Group Theoretical Description of Mendeleev Periodic System