The Birman-Murakami-Wenzl algebras of type E
n |
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| Authors: | Arjeh M Cohen David B Wales |
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| Institution: | (1) Department of Mathematical Sciences, King’s College, Aberdeen University, Meston Building, AB24 3UE Aberdeen, Scotland, UK |
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| Abstract: | The Birman-Murakami-Wenzl algebras (BMW algebras) of type E
n
for n = 6; 7; 8 are shown to be semisimple and free over the integral domain
\mathbbZ d±1,l±1,m ] | / |
( m( 1 - d ) - ( l - l - 1 ) ) {{{\mathbb{Z}\left {{\delta^{\pm 1}},{l^{\pm 1}},m} \right]}} \left/ {{\left( {m\left( {1 - \delta } \right) - \left( {l - {l^{ - 1}}} \right)} \right)}} \right.} 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 E
n
is a homomorphic ring image and is also semisimple and free of the same rank as an algebra over the ring
\mathbbZ d±1 ] \mathbb{Z}\left {{\delta^{\pm 1}}} \right] . 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 E
n
share many structural properties with the classical ones (of type A
n
) and those of type D
n
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| Keywords: | |
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