Degenerations of Jordan Algebras and ``Marginal{''} Algebras

Author(s)

Gorshkov, Ilya ^[1] ; Kaygorodov, Ivan ^[2] ; Popov, Yury ^[3]

Affiliation

^[1] Sobolev Inst Math, Novosibirsk - Russia

^[2] Univ Fed ABC, CMCC, Santo Andre, SP - Brazil

^[3] Univ Estadual Campinas, Campinas - Brazil

• Document type: Journal article
• Source: ALGEBRA COLLOQUIUM; v. 28, n. 02, p. 281-294, JUN 2021.
• Web of Science Citations: 0

Abstract

We describe all degenerations of the variety Jord(3) of Jordan algebras of dimension three over C. In particular, we describe all irreducible components in Jord(3). For every n we define an n-dimensional rigid ``marginal{''} Jordan algebra of level one. Moreover, we discuss marginal algebras in associative, alternative, left alternative, non-commutative Jordan, Leibniz and anticommutative cases. (AU)

• FAPESP's process: 18/15712-0 - Conservative algebras and superalgebras
• Grantee: Ivan Kaygorodov
• Support Opportunities: Regular Research Grants
• FAPESP's process: 16/16445-0 - Representations of (super)algebras of Jordan type
• Grantee: Yury Popov
• Support Opportunities: Scholarships in Brazil - Doctorate