Quantum group structures associated with invariances of some physical algebras

Abstract

In this study, the anticommuting spin algebra is introduced and it is shownto be invariant under the action of the quantum group SOq=-1(3). Furthermore, itsrepresentations and Hopf algebra structure are studied and found to be closely resemble the similar results for the angular momentum algebra. The invariance propertiesof the bosonic and fermionic oscillator algebras under inhomogeneous transformationsare also studied. The bosonic inhomogeneous symplectic group, BISp(2d,R) , andthe fermionic inhomogeneous orthogonal group, FIO(2d,R) , are defined as the inhomogeneous invariance quantum groups of these algebras. The sub(quantum)groupsand contractions of these quantum groups are studied as a source for new quantumgroups. Finally, the fermionic inhomogeneous orthogonal quantum group is defined forodd number of dimensions and its sub(quantum)groups and contractions are studied.