The Burman-Murakami-Wenzl algebras of type En
Transformation Groups(2011)
摘要
The Birman-Murakami-Wenzl algebras (BMW algebras) of type En for n=6,7,8 are
shown to be semisimple and free over a quotient of a polynomial algebra of
ranks 1,440,585; 139,613,625; and 53,328,069,225. We also show they are
cellular over suitable rings. The Brauer algebra of type En is a homomorphic
ring image and is also semisimple and free of the same rank as an algebra over
a different polynomial ring. A rewrite system for the Brauer algebra is used in
bounding the rank of the BMW algebra above. The generalized Temperley-Lieb
algebra of type En turns out to be a subalgebra of the BMW algebra of the same
type. So, the BMW algebras of type En share many structural properties with the
classical ones (of type An) and those of type Dn.
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关键词
brauer algebra,cellular algebra,semisimple algebra,root system,coxeter group,birman-murakami-wenzl algebra,word problem in semigroups,associative algebra,generalized temperley-lieb algebra,bmw alge- bra
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