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

 

Quadratic differential equations
in $\mathbb Z _{2}$-graded algebras


Authors: Nora C. Hopkins and Michael K. Kinyon
Journal: Trans. Amer. Math. Soc. 351 (1999), 4545-4559
MSC (1991): Primary 34C35, 17A60, 34C20, 17A36
Published electronically: July 19, 1999
MathSciNet review: 1475685
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Abstract | References | Similar Articles | Additional Information

Abstract: Quadratic differential equations whose associated algebra has an automorphism of order two are studied. Under hypotheses that naturally generalize the cases where the even or odd part of the algebra is one dimensional, the following are examined: structure theory of the associated algebra (ideal structure, simplicity, solvability, and nilpotence), derivations and first integrals, trajectories given by derivations, and Floquet decompositions.


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Additional Information

Nora C. Hopkins
Affiliation: Department of Mathematics and Computer Science, Indiana State University, Terre Haute, Indiana 47809
Email: hopkins@laurel.indstate.edu

Michael K. Kinyon
Affiliation: Department of Mathematics and Computer Science, Indiana University South Bend, South Bend, Indiana 46634
Email: mkinyon@iusb.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02212-6
PII: S 0002-9947(99)02212-6
Received by editor(s): October 1, 1996
Received by editor(s) in revised form: June 2, 1997
Published electronically: July 19, 1999
Article copyright: © Copyright 1999 American Mathematical Society