Affine Birman–Wenzl–Murakami algebras and tangles in the solid torus
Volume 190 / 2006
Fundamenta Mathematicae 190 (2006), 77-137 MSC: 57M25, 81R50. DOI: 10.4064/fm190-0-4
The affine Birman–Wenzl–Murakami algebras can be defined algebraically, via generators and relations, or geometrically as algebras of tangles in the solid torus, modulo Kauffman skein relations. We prove that the two versions are isomorphic, and we show that these algebras are free over any ground ring, with a basis similar to a well known basis of the affine Hecke algebra.