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
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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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- S. König and C. C. Xi, A characteristic free approach to Brauer algebras. Preprint 98–005, Bielefeld, 1998.
- S. König and C. C. Xi, When is a cellular algebra quasi-hereditary? Preprint 98–089, Bielefeld, 1998.
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- R. Brauer, On algebras which are connected with the semisimple continous groups. Annals of Math. 38, 854–872 (1937).
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- V. Dlab and C. M. Ringel, Quasi-hereditary algebras. Illinois J.Math. 33, 280–291 (1989).
- S. Donkin, On Schur algebras and related algebras I. J. Alg. 104, 310–328 (1986).
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- S. König and C. C. Xi, Cellular algebras: inflations and Morita equivalences. Preprint 97–078, Bielefeld, 1997. To appear in Journal of the London Math. Society.
- S. König and C. C. Xi, On the number of cells of a cellular algebra. Preprint 97–126, Bielefeld, 1997. To appear in Comm. in Algebra.
- S. König and C. C. Xi, A characteristic free approach to Brauer algebras. Preprint 98–005, Bielefeld, 1998.
- S. König and C. C. Xi, When is a cellular algebra quasi-hereditary? Preprint 98–089, Bielefeld, 1998.
- S. König and C. C. Xi, A self-injective cellular algebra is weakly symmetric. Preprint 99–017, Bielefeld, 1999.
- P. P. Martin, The structure of the partition algebras. J. Algebra 183, 319–358 (1996).
- B. Parshall and L. Scott, Derived categories, quasi-hereditary algebras and algebraic groups. Proc. of the Ottawa–Moosonee Workshop in Algebra 1987, Math. Lecture Note Series, Carleton University and Université d’Ottawa (1988).
- H. Wenzl, On the structure of Brauer’s centralizer algebras. Annals of Math. 128, 173–193 (1988).
- C. C. Xi, Partition algebras are cellular. To appear in Compos. Math.
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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
