C*-quantum groups with projection
by Sutanu Roy
Date of Examination:2013-09-26
Date of issue:2014-06-25
Advisor:Prof. Dr. Ralf Meyer
Referee:Prof. Dr. Ralf Meyer
Referee:Prof. Dr. Dorothea Bahns
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EnglishWe propose a general theory to study semidirect products of C -quantum groups in the framework of multiplicative unitaries. Starting from a quantum group with a projection we decompose its multiplicative unitary as a product of two unitary operators. One of them is again a multiplicative unitary in the standard sense; it describes the quotient. The other unitary is multiplicative in a braided sense; it corresponds to the kernel of the projection. Conversely, starting from a standard multiplicative unitary and a braided multiplicative unitary acting on different Hilbert spaces we construct a standard multiplicative unitary acting on the tensor product of them. Basic tools used to achieve this contain the interpretation of bicharacters as homomorphisms between quantum groups, generalised crossed products of C -algebras carrying coactions of quasitriangular quantum groups (quantum groups with a unitary R-matrix), and Yetter–Drinfeld C -algebras.
Keywords: C*-algebra, quantum group, bicharacter, crossed product, R-matrix, braided multiplicative unitary.