Idempotent Geometry in Generic Algebras

Yakov Krasnov, Vladimir G. Tkachev

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Using the syzygy method, established in our earlier paper (Krasnov and Tkachev, Honor of Wolfgang SprßigTrends Math, Birkhäuser/Springer Basel AG, Basel, 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.

Original languageEnglish
Article number84
JournalAdvances in Applied Clifford Algebras
Issue number5
StatePublished - 1 Nov 2018

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© 2018, The Author(s).


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