The method used to construct the bicovariant bimodule in ref. [CSWW] is applied to examine the structure of the dual algebra and the bicovariant differential calculus of the complex quantum group. The complex quantum group Funq(SL(N, C)) is defined by requiring that it contains Funq(SU(N)) as a subalgebra analogously to the quantum Lorentz group. Analyzing the properties of the fundamental bimodule, we show that the dual algebra has the structure of the twisted product Funq(SU(N))⊗Funq(SU(N))reg*. Then the bicovariant differential calculi on the complex quantum group are constructed.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics