Cyclotomic Birman--Wenzl--Murakami algebras, II: Admissibility Relations and Freeness

Abstract

The cyclotomic Birman-Wenzl-Murakami algebras are quotients of the affine BMW algebras in which the affine generator satisfies a polynomial relation. We study admissibility conditions on the ground ring for these algebras, and show that the algebras defined over an admissible integral ground ring $S$ are free $S$--modules and isomorphic to cyclotomic Kauffman tangle algebras. We also determine the representation theory in the generic semisimple case, obtain a recursive formula for the weights of the Markov trace, and give a sufficient condition for semisimplicity.

Stylistic corrections; changed numbering of sections; changed title

References in corpus (1)

• The Cyclotomic Birman-Murakami-Wenzl Algebras

Cited by in corpus (2)

• Cellularity of Cyclotomic Birman--Wenzl--Murakami algebras
• Cyclotomic Birman--Wenzl--Murakami algebras, I: Freeness and realization as tangle algebras