THE BIRMAN–MURAKAMI–WENZL ALGEBRAS OF TYPE Dn
نویسندگان
چکیده
The Birman–Murakami–Wenzl algebra (BMW algebra) of type Dn is shown to be semisimple and free over Z[δ±1, l±1]/(m(1− δ)− (l− l−1)) of rank (2n + 1)n!! − (2n−1 + 1)n!, where n!! = 1 · 3 · · · (2n − 1). We also show it is a cellular algebra over suitable rings. The Brauer algebra of type Dn is a homomorphic ring image and is also semisimple and free of the same rank, but over the ring Z[δ±1]. A rewrite system for the Brauer algebra is used in bounding the rank of the BMW algebra above. 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, Birman–Murakami–Wenzl algebra, BMW algebra, Brauer algebra, cellular algebra, Coxeter group, generalized Temperley–Lieb algebra, root system, semisimple algebra, word problem in semigroups AMS 2000 Mathematics Subject Classification: 16K20, 17Bxx, 20F05, 20F36, 20M05
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