#### 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).

Done