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Stably thick subcategories of modules over Hopf algebras

Published online by Cambridge University Press:  18 May 2001

MARK HOVEY  and
JOHN H. PALMIERI
MARK HOVEY
Affiliation:
Department of Mathematics, Wesleyan University, Middletown, CT 06459, U.S.A. e-mail: hovey@member.ams.org
JOHN H. PALMIERI
Affiliation:
Department of Mathematics, University of Washington, Seattle, WA 98195, U.S.A. e-mail: palmieri@member.ams.org
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Abstract

We discuss a general method for classifying certain subcategories of the category of finite-dimensional modules over a finite-dimensional co-commutative Hopf algebra B. Our method is based on that of Benson–Carlson–Rickard [BCR1], who classify such subcategories when B = kG, the group ring of a finite group G over an algebraically closed field k. We get a similar classification when B is a finite sub-Hopf algebra of the mod 2 Steenrod algebra, with scalars extended to the algebraic closure of F2. Along the way, we prove a Quillen stratification theorem for cohomological varieties of modules over any B, in terms of quasi-elementary sub-Hopf algebras of B.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 130 , Issue 3 , May 2001 , pp. 441 - 474
Copyright
2001 Cambridge Philosophical Society

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