Classification of nilpotent evolution algebras and extensions of their derivations. Issue 10 (2nd October 2020)

• Record Type: Journal Article
• Authors: Mukhamedov, Farrukh; Khakimov, Otabek; Qaralleh, Izzat
• Is Part Of: Communications in algebra. Volume 48:Issue 10(2020)
• Page Start: 4155
• Page End: 4169
• Publication Date: 2020-10-02
• Subjects: Classification -- derivation -- evolution algebra -- extension; 17A60 -- 17A36 -- 17D92 -- 47B39; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2020.1757688
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: This article is devoted to n -dimensional nilpotent finite-dimensional evolution algebras E with maximal index of nilpotency. We are able to find full invariants of these algebras which allows us to classify them. Furthermore, we explicitly describe its associative enveloping algebras. Moreover, we give an affirmative answer to the question: is it possible to extend a given derivation of the nilpotent evolution algebra to its enveloping algebra.