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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hereditary crossed products


Authors: Jeremy Haefner and Gerald Janusz
Journal: Trans. Amer. Math. Soc. 352 (2000), 3381-3410
MSC (1991): Primary 16G30, 16H05, 16S35, 16W20, 16W50
Published electronically: March 27, 2000
MathSciNet review: 1661242
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Abstract: We characterize when a crossed product order over a maximal order in a central simple algebra by a finite group is hereditary. We need only concentrate on the cases when the group acts as inner automorphisms and when the group acts as outer automorphisms. When the group acts as inner automorphisms, the classical group algebra result holds for crossed products as well; that is, the crossed product is hereditary if and only if the order of the group is a unit in the ring. When the group is acting as outer automorphisms, every crossed product order is hereditary, regardless of whether the order of the group is a unit in the ring.


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Additional Information

Jeremy Haefner
Affiliation: Department of Mathematics, University of Colorado, Colorado Springs, Colorado 80933
Email: haefner@math.uccs.edu

Gerald Janusz
Affiliation: Department of Mathematics, University of Illinois, Champaign-Urbana, Illinois 61801
Email: janusz@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02476-4
PII: S 0002-9947(00)02476-4
Keywords: Order, finite representation type, hereditary crossed products, automorphisms
Received by editor(s): February 23, 1998
Published electronically: March 27, 2000
Additional Notes: The first author was partially supported by a grant from the National Security Agency
Article copyright: © Copyright 2000 American Mathematical Society