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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.

Copyright 1999 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 05 (1999), pp. 71-75
• Publisher Identifier: S 1079-6762(99)00063-3
• 1991 Mathematics Subject Classification. Primary 16D80, 16G30, 20C30, 20G05; Secondary 16D25, 18G15, 20F36, 57M25, 81R05
• Key words and phrases.
• Received by the editors March 15, 1999
• Posted on June 24, 1999
• Communicated by Dave Benson
• Comments (When Available)

Steffen König

Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany

E-mail address: koenig@mathematik.uni-bielefeld.de

Changchang Xi

Department of Mathematics, Beijing Normal University, 100875 Beijing, P. R. China

E-mail address: xicc@bnu.edu.cn

The research of C.C. Xi was partially supported by NSF of China (No. 19831070).