Complex Structures in Real Algebras. I. Two-Dimensional Commutative Case

We study complex structures in real two-dimensional commutative algebras and show their connection with homotopy properties of the multiplications. An application to the Riccati equation in rank three algebras is also discussed.

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Bibliographic Details
Published in:Communications in algebra 2003-01, Vol.31 (9), p.4571-4609
Main Authors: Balanov, Zalman, Krasnov, Yakov
Format: Article
Language:English
Subjects:
Complex structures
Non-associative algebras
Polynomial equations in algebra
Primary 58E05, 58E09
Quadratic maps
Secondary 35J20
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Description
Summary:We study complex structures in real two-dimensional commutative algebras and show their connection with homotopy properties of the multiplications. An application to the Riccati equation in rank three algebras is also discussed.
ISSN:0092-7872
1532-4125
DOI:10.1081/AGB-120022810