Classification of nilpotent evolution algebras and extensions of their derivations
Farrukh MukhamedovDepartment of Mathematical Sciences, College of Science, The United Arab Emirates University, Al Ain, Abu Dhabi, UAE;Otabek KhakimovIzzat QarallehDepartment of Mathematics, Faculty of Science, Tafila Technical University, Tafila, Jordan
2020en
ABI
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.
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Cited by 20 references