Geodesic
Cellular algebras and quasi-hereditary algebras: a comparison
König, Steffen1 ; Xi, Changchang2
1 Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
2 Department of Mathematics, Beijing Normal University, 100875 Beijing, P. R. China
Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 71-75.

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S1079-6762-99-00063-3

König, Steffen 1 ; Xi, Changchang 2

1 Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
2 Department of Mathematics, Beijing Normal University, 100875 Beijing, P. R. China 
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König, Steffen; Xi, Changchang. Cellular algebras and quasi-hereditary algebras: a comparison. Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 71-75. doi : 10.1090/S1079-6762-99-00063-3. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-99-00063-3/

[1] Bernšteĭn, I. N., Gel′Fand, I. M., Gel′Fand, S. I. A certain category of 𝔤-modules Funkcional. Anal. i Priložen. 1976 1 8

[2] Cline, E., Parshall, B., Scott, L. Finite-dimensional algebras and highest weight categories J. Reine Angew. Math. 1988 85 99

[3] Dlab, Vlastimil, Ringel, Claus Michael Quasi-hereditary algebras Illinois J. Math. 1989 280 291

[4] Donkin, S. On Schur algebras and related algebras. I J. Algebra 1986 310 328

[5] Graham, J. J., Lehrer, G. I. Cellular algebras Invent. Math. 1996 1 34

[6] Martin, Paul The structure of the partition algebras J. Algebra 1996 319 358

[7] Wenzl, Hans On the structure of Brauer’s centralizer algebras Ann. of Math. (2) 1988 173 193

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