Genetic Volterra algebras and their derivations
Rasul GanikhodzhaevFaculty of Mechanics and Mathematics, National University of Uzbekistan, Vuzgorodok, Tashkent, UzbekistanFarrukh MukhamedovDepartment of Mathematical Sciences, College of Science, The United Arab Emirates University, Al Ain, Abu Dhabi, UAEAbror PirnapasovDepartment of Mathematics, The Abdus Salam International Centre for Theoretical Sciences, Trieste, ItalyIzzat QarallehFaculty of Science, Department of Mathematics, Tafila Technical University, Tafila, Jordan
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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.
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