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Fundamental automorphisms of Clifford algebras and an extension of Dabrowski Pin groups. (English) Zbl 1041.81538
Summary: 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 played 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 the case of odd-dimensional spaces. Application potentialities of the introduced quotient groups in physics are discussed.

81R25 Spinor and twistor methods applied to problems in quantum theory
15A66 Clifford algebras, spinors