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

Full-text PDF Free Access

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