Complex structures in algebra, topology and differential equations

Zalman Balanov, Yakov Krasnov

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In this paper, we present our recent results on the so-called complex structures in algebras in the context relevant to the following four problems which, at first glance, have nothing in common: (i) solubility of polynomial equations in non-associative algebras, (ii) topological/geometric properties of quadratic maps, (iii) existence of bounded solutions to quadratic differential systems, and (iv) ellipticity of the Dirac equation. The unsolved problems related to (i)-(iv) are formulated as well.

Original languageEnglish
Pages (from-to)249-260
Number of pages12
JournalGeorgian Mathematical Journal
Issue number3
StatePublished - 1 Sep 2014

Bibliographical note

Publisher Copyright:
© 2014 by De Gruyter 2014.


  • Real quadratic polynomial map
  • complex structures
  • isotopy
  • non-associative algebras


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