Idempotent geometry in generic algebras
Rings and Algebras
2018-09-12 v2 Commutative Algebra
Dynamical Systems
Abstract
Using the syzygy method, established in our earlier paper, 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.
Cite
@article{arxiv.1802.04994,
title = {Idempotent geometry in generic algebras},
author = {Yakov Krasnov and Vladimir G. Tkachev},
journal= {arXiv preprint arXiv:1802.04994},
year = {2018}
}
Comments
17 pages, 3 figures, submitted (some typos corrected)