Last updates: 13 April 2011
The affine braid group is the group given by generators and , with relations
The affine braid group is isomorphic to the group of braids in the thickened annulus (see, for example [GH2]), where the generators and are identified with the diagrams
The pictorial computation PUTTHISPICTUREIN shows that the all commute with each other.
This section is based on forthcoming joint work with Z. Daugherty and R. Virk [DRV]. See [GH2] or [OR] for pictures of braids in an annulus, or in a cylinder.
[Bou] N. Bourbaki, Groupes et Algèbres de Lie, Masson, Paris, 1990.
[GH1] F. Goodman and H. Hauschild Mosley, Cyclotomic Birman-Wenzl-Murakami algebras. I. Freeness and realization as tangle algebras, J. Knot Theory Ramifications 18 (2009), 1089-1127. MR2554337 (2010j:57014)
[OR] R. Orellana and A. Ram, Affine braids, Markov traces and the category , Algebraic groups and homogeneous spaces, 423-473, Tata Inst. Fund. Res. Stud. Math., Tata Inst. Fund. Res., Mumbai, 2007. MR2348913 (2008m:17034)