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Simple Compact Quantum Groups I | | Shuzhou Wang
; | | Date: |
31 Oct 2008 | | Abstract: | The notion of simple compact quantum group is introduced. As non-trivial
(noncommutative and noncocommutative) examples, the following families of
compact quantum groups are shown to be simple: (a) The universal quantum groups
$B_u(Q)$ for $Q in GL(n, {mathbb C})$ satisfying $Q ar{Q} = pm I_n$, $n
geq 2$; (b) The quantum automorphism groups $A_{aut}(B, au)$ of finite
dimensional $C^*$-algebras $B$ endowed with the canonical trace $ au$ %endowed
with a tracial functional $tr$ when $dim(B) geq 4$, including the quantum
permutation groups $A_{aut}(X_n)$ on $n$ points ($n geq 4$); (c) The standard
deformations $K_q$ of simple compact Lie groups $K$ and their twists $K_q^u$,
as well as Rieffel’s deformation $K_J$. | | Source: | arXiv, 0810.5734 | | Services: | Forum | Review | PDF | Favorites | |
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