Quantum Braided Clifford Algebras

Abstract

We propose a natural generalization of general linear inhomogeneous groups as quantum braided groups. This generalization is in the spirit of the theory initiated and developed by S. Majid, however, our construction differs in the interrelation between the homogeneous and inhomogeneous parts of the group. In order to define the quantum braided orthogonal groups, we introduce a kind of quantum geometry in the covector space. This enables us to introduce in a natural way a quantum braided Clifford algebra structure related to the spinor representation of that group.