A Temperley-lieb Analogue for the Bmw Algebra
نویسنده
چکیده
The Temperley-Lieb algebra may be thought of as a quotient of the Hecke algebra of type A, acting on tensor space as the commutant of the usual action of quantum sl2 on (C(q) ). We define and study a quotient of the BirmanWenzl-Murakami algebra, which plays an analogous role for the 3-dimensional representation of quantum sl2. In the course of the discussion we prove some general results about the radical of a cellular algebra, which may be of independent interest.
منابع مشابه
The Bmw Algebras of Type
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 ...
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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 r...
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