Braided Chains of q-Deformed Heisenberg Algebrae

Abstract

Given M copies of a q-deformed Weyl or Clifford algebra in the defining representation of a quantum group $G_q$, we determine a prescription to embed them into a unique, inclusive $G_q$-covariant algebra. The different copies are "coupled" to each other and are naturally ordered into a "chain". In the case $G_q=SL_q(N)$ a modified prescription yields an inclusive algebra which is even explicitly $SL_q(M) X SL_q(N)$-covariant, where $SL_q(M)$ is a symmetry relating the different copies. By the introduction of these inclusive algebrae we significantly enlarge the class of $G_q$-covariant deformed Weyl/Clifford algebrae available for physical applications.