## Quadratic differential equations in $\mathbb {Z}_2$-graded algebras

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- by Nora C. Hopkins and Michael K. Kinyon PDF
- Trans. Amer. Math. Soc.
**351**(1999), 4545-4559 Request permission

## 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.## References

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## Additional Information

**Nora C. Hopkins**- Affiliation: Department of Mathematics and Computer Science, Indiana State University, Terre Haute, Indiana 47809
- MR Author ID: 217047
- Email: hopkins@laurel.indstate.edu
**Michael K. Kinyon**- Affiliation: Department of Mathematics and Computer Science, Indiana University South Bend, South Bend, Indiana 46634
- MR Author ID: 267243
- ORCID: 0000-0002-5227-8632
- Email: mkinyon@iusb.edu
- Received by editor(s): October 1, 1996
- Received by editor(s) in revised form: June 2, 1997
- Published electronically: July 19, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**351**(1999), 4545-4559 - MSC (1991): Primary 34C35, 17A60, 34C20, 17A36
- DOI: https://doi.org/10.1090/S0002-9947-99-02212-6
- MathSciNet review: 1475685