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In this paper, we give the complete classification of 5-dimensional complex solvable symmetric Leibniz algebras. [ABSTRACT FROM AUTHOR]

In the paper, we describe the automorphisms on the solvable Leibniz algebras with the model or abelian nilradicals, whose complementary spaces are equal to two and one, respectively. We show that any local automorphism on a solvable Leibniz algebra with model nilradical of maximal codimension is an automorphism. We show that solvable Leibniz algebras with abelian nilradicals, which have 1-dimension complementary space, admit local automorphisms which are not automorphisms. Moreover, similar problems concerning 2-local automorphisms of such algebras are investigated. We give examples of solvable Leibniz algebras in which 2-local automorphisms are automorphisms and examples of such algebras which admit 2-local automorphisms which are not automorphisms. [ABSTRACT FROM AUTHOR]

We are interested in the evolution operators defined on commutative and non-associative algebras when the characteristic of the scalar field is 2. We distinguish four types: nilpotent, quasi-constant, ultimately periodic, and plenary train operators. They are studied and classified for non-baric and for baric algebras. [ABSTRACT FROM AUTHOR]

We show that any local derivation on the solvable Leibniz algebras with model or abelian nilradicals, whose dimension of complementary space is maximal is a derivation. We show that solvable Leibniz algebras with abelian nilradicals, which have 1 dimension complementary space, admit local derivations which are not derivations. Moreover, similar problem concerning 2 -local derivations of such algebras is investigated and an example of solvable Leibniz algebra is given such that any 2 -local derivation on it is a derivation, but which admits local derivations which are not derivations. [ABSTRACT FROM AUTHOR]