The Bmw Algebras of Type
نویسنده
چکیده
The Birman-Murakami-Wenzl algebra (BMW algebra) of type Dn is shown to be semisimple and free over Z[δ, l]/(m(1 − δ) − (l − l)) of dimension (2n +1)n!!− (2 +1)n!, where n!! = 1 ·3 · · · (2n−1). The Brauer algebra of type Dn is a homomorphic ring image and is also semisimple and free of the same dimension, but over the ring Z[δ]. A rewrite system for the Brauer algebra is used in upper bounding the dimension of the BMW algebra. As a consequence of our results, the generalized Temperley-Lieb algebra of type Dn turns out to be a subalgebra of the BMW algebra of the same type. keywords: associative algebra, BMW algebra, Brauer algebra, word problem in semigroups, semisimple algebras, generalized Temperley-Lieb algebra, root systems, Coxeter groups, AMS 2000 Mathematics Subject Classification: 16K20, 17Bxx, 20F05, 20F36, 20M05
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