. G T ] 1 9 A ug 2 00 5 Braid Groups of the Sun Graph

Bgp-reflection Functors and Lusztig's Symmetries: a Ringel-hall Algebra Approach to Quantum Groups

According to the canonical isomorphisms between the Ringel-Hall algebras (composition algebras) and the quantum groups, we deduce the Lusztig's symmetries T 00 i;1 , i 2 I, by applying the Bernstein-Gelfand-Ponomarev reeection functors to the Drinfeld doubles of Ringel-Hall algebras. The fundamental properties of T 00 i;1 including the following can be obtained conceptually, (1). T 00 i;1 induc...

ar X iv : m at h / 05 01 05 1 v 2 [ m at h . G R ] 1 7 M ay 2 00 6 INJECTIONS OF ARTIN GROUPS

We study those Artin groups which, modulo their centers, are finite index subgroups of the mapping class group of a sphere with at least 5 punctures. In particular, we show that any injective homomorphism between these groups is parameterized by a homeomorphism of a punctured sphere together with a map to the integers. We also give a generating set for the automorphism group of the pure braid g...

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

ar X iv : m at h / 02 10 26 0 v 1 [ m at h . Q A ] 1 7 O ct 2 00 2 On representations of braid groups determined by directed graphs 1

We show that any Markov L-coalgebra, i.e. a k-vector space equipped with two coproducts representing a directed graph yields a solution of the Yang-Baxter equation and thus a representation of braid groups. If the directed graph is equipped with a family of probability vectors then such family yields also a representation of braid groups. We end by a generalisation of these construction to any ...

ar X iv : s ol v - in t / 9 80 80 13 v 1 2 4 A ug 1 99 8 On fusion algebra of chiral SU ( N ) K models

We discuss some algebraic setting of chiral SU (N) K models in terms of the satistical dimensions of their fields. In particular, the conformal dimensions and the central charge of the chiral SU (N) K models are calculated from their braid matrices. Furthermore, at level K = 2, we present the characteristic polynomials of their fusion matrices in a factored form.