Quantum group contraction and bosonisation

Abstract: Abstract: In 1953 İnönü and Wigner introduced group contraction: a systematic (limiting) process to obtain from a given Lie group a non-isomorphic Lie group. For example, the contraction of SU(2) group (with respect to its closed subgroup T) is isomorphic to the double cover of E(2) group. The q-deformed C*-algebraic analogue of this example was introduced and investigated by Woronowicz during the mid '80s to early '90s. More precisely, the C*-algebraic deformations of SU(2) and (the double cover of) E(2) with respect to real deformation parameters 0<|q|<1 become compact (denoted by SUq(2)) and non-compact locally compact (denoted by Eq(2)) quantum groups, respectively. Furthermore, the contraction of SUq(2) groups becomes (isomorphic) to Eq(2) groups. However, for complex deformation parameters 0<|q|<1, the objects SUq(2) and Eq(2) are not ordinary but braided quantum groups. More generally, the quantum analogue of the normal subgroup of a semidirect product group becomes a braided quantum group and the reconstruction process of the semidirect product quantum group from a braided quantum group is called bosonisation. In this talk, we shall present a braided version of the contraction procedure between SUq(2) and Eq(2) groups (for complex deformation parameters 0<|q|<1) and address its compatibility with bosonisation. This is based on a joint work with Atibur Rahaman.

functional analysisoperator algebras

Audience: researchers in the topic

Webinars on Operator Theory and Operator Algebras