Alladi Ramakrishnan Hall

Braided C*-quantum groups

Dr. Sutanu Roy

Carleton University, Canada

Semidirect product decomposition of a group K is equivalent to an
idempotent homomorphism or projection p on K, and K is isomorphic to the
semidirect product of Im(p) acting on Ker(p). Quantum groups with
projection are the noncommutative analogue of semidirect products of
groups. Radford’s Theorem about Hopf algebras with projection suggests that
any quantum group K with projection p decomposes uniquely into an ordinary
quantum group G (corresponds to the image of p) and a "braided" quantum
group H over G (corresponds to the kernel of p) and vice versa. In this
talk, we establish this equivalence in the C*-algebraic framework. We shall
also briefly discuss two examples of braided C*-quantum groups over circle,
namely q-deformation (q is non-zero complex number) of SU(2) (which is
compact) and quantum plane (which is locally compact).