En型Burman-Murakami-Wenzl代数
The Burman-Murakami-Wenzl algebras of type En
摘要：
本文证明了n= 6，7，8的En型Birman-Murakami-Wenzl代数（BMW代数）在秩为1，440，585、139，613，625和53，328，069，225的多项式代数的商上是半单的和自由的。我们还表明，他们是细胞适当的环。En型Brauer代数是一个同态环象，也是半单的，并且与不同多项式环上的代数没有相同的秩。一个重写系统的Brauer代数是用来界定秩的宝马代数以上。证明了En型广义Temperley-Lieb代数是同类型BMW代数的一个子代数。因此，En型BMW代数与经典的An型BMW代数和Dn型BMW代数具有许多结构性质。
英文摘要：
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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