ar X iv : 0 71 1 . 14 20 v 1 [ m at h . O A ] 9 N ov 2 00 7 Finite - dimensional Hopf C - bimodules and C - pseudo - multiplicative unitaries

ar X iv : 0 70 9 . 46 17 v 1 [ m at h . O A ] 2 8 Se p 20 07 C - pseudo - Kac systems and duality for coactions of concrete

We study coactions of concrete Hopf C -bimodules in the framework of (weak) C pseudo-Kac systems, define reduced crossed products and dual coactions, and prove an analogue of Baaj-Skandalis duality.

C∗-pseudo-multiplicative unitaries

We introduce C∗-pseudo-multiplicative unitaries and (concrete) Hopf C∗-bimodules, which are C∗-algebraic variants of the pseudo-multiplicative unitaries on Hilbert spaces and the Hopf-von Neumann-bimodules studied by Enock, Lesieur, and Vallin [5, 6, 4, 10, 19, 20]. Moreover, we associate to every regular C∗-pseudo-multiplicative unitary two Hopf-C∗bimodules and discuss examples related to loca...

C-pseudo-multiplicative unitaries and Hopf C-bimodules

We introduce C∗-pseudo-multiplicative unitaries and concrete Hopf C∗-bimodules for the study of quantum groupoids in the setting of C∗-algebras. These unitaries and Hopf C∗-bimodules generalize multiplicative unitaries and Hopf C∗-algebras and are analogues of the pseudo-multiplicative unitaries and Hopf–von Neumann-bimodules studied by Enock, Lesieur and Vallin. To each C∗-pseudo-multiplicativ...

ar X iv : m at h / 06 02 50 8 v 2 [ m at h . G R ] 1 9 N ov 2 00 7 PRESENTATIONS OF FINITE SIMPLE GROUPS : A QUANTITATIVE APPROACH

There is a constant C 0 such that all nonabelian finite simple groups of rank n over Fq, with the possible exception of the Ree groups 2 G 2 (3 2e+1), have presentations with at most C 0 generators and relations and total length at most C 0 (log n + log q). As a corollary, we deduce a conjecture of Holt: there is a constant C such that dim H 2 (G, M) ≤ C dim M for every finite simple group G, e...

ar X iv : 0 71 1 . 23 72 v 1 [ m at h . G R ] 1 5 N ov 2 00 7 Braid groups and Artin groups