Jordan algebras admitting derivations with invertible values

Author(s)

Kaygorodov, Ivan ^[1] ; Lopatin, Artem ^{[2, 3]} ; Popov, Yury ^{[4, 2]}

Affiliation

^[1] Univ Fed ABC, CMCC, Santo Andre, SP - Brazil

^[2] Univ Estadual Campinas, IMECC, Campinas, SP - Brazil

^[3] Sobolev Inst Math, Omsk Branch, Omsk - Russia

^[4] Novosibirsk State Univ, Novosibirsk - Russia

• Document type: Journal article
• Source: COMMUNICATIONS IN ALGEBRA; v. 46, n. 1, p. 69-81, 2018.
• Web of Science Citations: 1

Abstract

The notion of a derivation with invertible values as a derivation of ring with unity that only takes multiplicatively invertible or zero values appeared in a paper of Bergen, Herstein and Lanski, in which they determined the structure of associative rings that admit derivations with invertible values. Later, the results of this paper were generalized in many cases, for example, for generalized derivations, associative superalgebras, alternative algebras and many others. The present work is dedicated to the description of all Jordan algebras admitting derivations with invertible values. (AU)

• FAPESP's process: 14/24519-8 - Generalized derivations of non associative 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
• FAPESP's process: 16/00541-0 - Properties of algebras of invariants
• Grantee: Artem Lopatin
• Support Opportunities: Regular Research Grants