Derivations and automorphisms of nilpotent evolution algebras with maximal nilindex
Farrukh MukhamedovDepartment of Mathematical Sciences, College of Science, The United Arab Emirates University, P. O. Box, 15551, Al Ain, Abu Dhabi, UAEOtabek KhakimovDepartment of Mathematical Sciences, College of Science, The United Arab Emirates University, P. O. Box, 15551, Al Ain, Abu Dhabi, UAEB. A. OmirovNational University of Uzbekistan, 4, University Street 100174, Tashkent, UzbekistanIzzat QarallehDepartment of Mathematics, Faculty of Science, Tafila Technical University, Tafila, Jordan
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This paper is devoted to the nilpotent finite-dimensional evolution algebras [Formula: see text] with [Formula: see text]. We describe the Lie algebra of derivations of these algebras. Moreover, in terms of these Lie algebras, we fully construct nilpotent evolution algebra with maximal index of nilpotency. Furthermore, this result allowed us fully characterize all local and 2-local derivations of the considered evolution algebras. Besides, all automorphisms and local automorphisms of these algebras are found.
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