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Hereditary crossed products
Author(s):
Jeremy
Haefner;
Gerald
Janusz
Journal:
Trans. Amer. Math. Soc.
352
(2000),
3381-3410.
MSC (1991):
Primary 16G30, 16H05, 16S35, 16W20, 16W50
Posted:
March 27, 2000
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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:
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
Posted:
March 27, 2000
Additional Notes:
The first author was partially supported by a grant from the National Security Agency
Copyright of article:
Copyright
2000,
American Mathematical Society
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