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

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

2006-12-02

arxiv.org/abs/math/0612065v5

Mathematics

Quantum Algebra

Stylistic corrections; changed numbering of sections; changed title

Scientific paper

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.

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