Genetic Volterra algebras and their derivations. Issue 3 (4th March 2018)

• Record Type: Journal Article
• Authors: Ganikhodzhaev, Rasul; Mukhamedov, Farrukh; Pirnapasov, Abror; Qaralleh, Izzat
• Is Part Of: Communications in algebra. Volume 46:Issue 3(2018)
• Page Start: 1353
• Page End: 1366
• Publication Date: 2018-03-04
• Subjects: Associative -- derivation -- generic algebra -- Volterra algebra; 17D92 -- 17D99 -- 60J10 -- 28D05; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2017.1347663
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: The present paper is devoted to genetic Volterra algebras. We first study characters of such algebras. We fully describe associative genetic Volterra algebras, in this case all derivations are trivial. In general setting, i.e., when the algebra is not associative, we provide a sufficient condition to get trivial derivation on generic Volterra algebras. Furthermore, we describe all derivations of three dimensional generic Volterra algebras, which allowed us to prove that any local derivation is a derivation of the algebra.