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-heredita
On the quasi-heredity and the semi-simplicity of cellular algebras
β Scribed by Yongzhi Cao
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 177 KB
- Volume
- 267
- Category
- Article
- ISSN
- 0021-8693
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β¦ Synopsis
Some simpler homological characterizations of quasi-hereditary algebras inside the class of cellular algebras are presented in terms of cell modules. Moreover, some new criteria for the semisimplicity of cellular algebras are given by using the cohomology groups of cell modules and simple modules.
π SIMILAR VOLUMES
Let R be a commutative algebra over a field k. We prove two related results on the simplicity of Lie algebras acting as derivations of R. If D is both a Lie subalgebra and R-submodule of Der k R such that R is D-simple and either char k = 2 or D is not cyclic as an R-module or D R = R, then we show