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Idempotent Geometry in Generic Algebras
Department of Mathematics, Bar-Ilan University, Ramat Gan, Israel.ORCID iD: 0000-0001-8274-3390
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-8422-6140
2018 (English)In: Advances in Applied Clifford Algebras, ISSN 0188-7009, E-ISSN 1661-4909, Vol. 28, no 5, article id UNSP 84Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Basel, Switzerland: Birkhaeuser Science , 2018. Vol. 28, no 5, article id UNSP 84
Keywords [en]
Idempotents
National Category
Algebra and Logic Geometry Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-150934DOI: 10.1007/s00006-018-0902-7ISI: 000443820100001OAI: oai:DiVA.org:liu-150934DiVA, id: diva2:1245602
Note

Funding agencies: G.S. Magnusons Foundation [MG 2017-0101]

Available from: 2018-09-05 Created: 2018-09-05 Last updated: 2018-12-03Bibliographically approved

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Tkachev, Vladimir

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