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Division algebras, (pseudo)orthogonal groups and spinors. (English) Zbl 0544.22010
A unified approach to the description of the groups $$SO(\nu-I)$$, $$SO(\nu)$$, $$SO(\nu+I)$$, $$SO(\nu+1,1)$$, and $$SO(\nu+2,2)$$ ($$\nu =1,2,4,8$$) and their spinor representations in terms of division algebras of real numbers, quaternions and octonions is developed. The obtained results are of special interest for the supersymmetric field theories with extra space-time dimensions.
Reviewer: A.Boguš.

##### MSC:
 22E50 Representations of Lie and linear algebraic groups over local fields 17A35 Nonassociative division algebras 15A75 Exterior algebra, Grassmann algebras 81T08 Constructive quantum field theory
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