2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/202815Classification 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-TEXHigh Energy Physics - Theorytext