Weyl–Brauer matrices

In mathematics, particularly in the theory of spinors, the Weyl–Brauer matrices are an explicit realization of a Clifford algebra as a matrix algebra of 2^⌊n/2⌋ × 2^⌊n/2⌋ matrices. They generalize the Pauli matrices to n dimensions, and are a specific construction of higher-dimensional gamma matrices. They are named for Richard Brauer and Hermann Weyl, and were one of the earliest systematic constructions of spinors from a representation theoretic standpoint.

The matrices are formed by taking tensor products of the Pauli matrices, and the space of spinors in n dimensions may then be realized as the column vectors of size 2^⌊n/2⌋ on which the Weyl–Brauer matrices act.