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Cellular algebras and quasi-hereditary algebras: a comparison


Authors: Steffen König and Changchang Xi
Journal: Electron. Res. Announc. Amer. Math. Soc. 5 (1999), 71-75
MSC (1991): Primary 16D80, 16G30, 20C30, 20G05; Secondary 16D25, 18G15, 20F36, 57M25, 81R05
DOI: https://doi.org/10.1090/S1079-6762-99-00063-3
Published electronically: June 24, 1999
MathSciNet review: 1696822
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Abstract | References | Similar Articles | Additional Information

Abstract: Cellular algebras have been defined in a computational way by the existence of a special kind of basis. We compare them with quasi-hereditary algebras, which are known to carry much homological and categorical structure. Among the properties to be discussed here are characterizations of quasi-hereditary algebras inside the class of cellular algebras in terms of vanishing of cohomology and in terms of positivity of the Cartan determinant.


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Additional Information

Steffen König
Affiliation: Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
MR Author ID: 263193
Email: koenig@mathematik.uni-bielefeld.de

Changchang Xi
Affiliation: Department of Mathematics, Beijing Normal University, 100875 Beijing, P. R. China
Email: xicc@bnu.edu.cn

Received by editor(s): March 15, 1999
Published electronically: June 24, 1999
Additional Notes: The research of C.C. Xi was partially supported by NSF of China (No. 19831070).
Communicated by: Dave Benson
Article copyright: © Copyright 1999 American Mathematical Society