Clifford Algebras of Polynomials Generalized Grassmann Algebras and q-Deformed Heisenberg Algebras

Abstract

Classification of finite dimensional representations of the q-deformed Heisenberg algebra $H_q(3)$ is made by the help of Clifford algebra of polynomials and generalized Grassmann algebra. Special attention is paid when $q$ is a primitive $n$ root of unity. As a further application we obtain finite dimensional representations of $sl(2{)}_q$ using its embedding into $H_q(3)$.

12 pages, CRN-94-17, PLAIN-TEX

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