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Notes on Weyl-Clifford algebras

Alexander Yu. Vlasov
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Abstract

Here is discussed generalization of Clifford algebras, l^n-dimensional Weyl-Clifford algebras T(n,l) with n generators t_k satisfying equation $(\sum_{k=1}^n a_k t_k)^l = \sum_{k=1}^n a_k^l$. It is originated from two basic and well known constructions: representation of Clifford algebras via tensor products of Pauli matrices together with extension for l > 2 using Weyl commutation relations. Presentation of such general topics here may not pretend to entire originality or completeness and it is rather a preliminary excursus into this very broad and interesting area of research.

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Alexander Yu. Vlasov. 2002-03-27. Notes on Weyl-Clifford algebras. https://arxiv.org/abs/math-ph/0112049

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