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  • 1.
    Krasnov, Yakov
    et al.
    Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel.
    Tkachev, Vladimir
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Idempotent Geometry in Generic Algebras2018In: Advances in Applied Clifford Algebras, ISSN 0188-7009, E-ISSN 1661-4909, Vol. 28, no 5, article id UNSP 84Article in journal (Refereed)
    Abstract [en]

    Using the syzygy method, established in our earlier paper (Krasnov and Tkachev, 2018), we characterize the combinatorial stratification of the variety of two-dimensional real generic algebras. We show that there exist exactly three different homotopic types of such algebras and relate this result to potential applications and known facts from qualitative theory of quadratic ODEs. The genericity condition is crucial. For example, the idempotent geometry in Clifford algebras or Jordan algebras of Clifford type is very different: such algebras always contain nontrivial submanifolds of idempotents.

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