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

DOI:
https://doi.org/10.1090/S0002-9947-00-02476-4

Published electronically:
March 27, 2000

MathSciNet review:
1661242

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-00-02476-4

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