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Spinor representations of *so*(*n*) algebras are obtained with the help of Clifford numbers. Starting from the definition of *SO*(*n*) as the group whose elements are orthogonal unimodular *n*x*n* matrices commutation relations that define the *so*(*n*) algebra are abstracted from the defining *n*-dimensional representation. Clifford numbers are defined and shown to be realizable in terms of 2* ^{m}*x2

*matrices. Explicit realizations are described. Next, the chapter defines the special Clifford number*

^{m}*γ*

_{2m+1}and use it to obtain spinor representations of

*so*(2

*m*+1) and semispinor representations of

*so*(2

*m*). Explicit results are given for

*so*(2),

*so*(3) and

*so*(4). The isomorphism between

*so*(4) and the direct sum of two

*so*(3)s is demonstrated. Biographical notes on Clifford and Schur are given.

*Keywords: *
Clifford numbers;
spinor;
semispinor

*Chapter.*
*4208 words.*

*Subjects: *
Mathematical and Statistical Physics

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