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On the Quasi-Heredity of Birman–Wenzl Algebras

✍ Scribed by Changchang Xi

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
280 KB
Volume
154
Category
Article
ISSN
0001-8708

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✦ Synopsis

In this paper we consider the Birman Wenzl algebras over an arbitrary field and prove that they are cellular in the sense of Graham and Lehrer. Furthermore, we determine for which parameters the Birman Wenzl algebras are quasi-hereditary. So the general theory of cellular algebras and quasi-hereditary algebras applies to Birman Wenzl algebras. As a consequence, we can determine all irreducible representations of the Birman Wenzl algebras by linear algebra methods. We prove also that the new Hecke algebras induced from Birman Wenzl algebras are Frobenius over a field (but not always cellular).

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