Manuel Ladra

CLASSIFICATION OF SOLVABLE LEIBNIZ ALGEBRAS WITH NULL-FILIFORM NILRADICAL

In this article we classify solvable Leibniz algebras whose nilradical is a null-filiform algebra. We extend the obtained classification to the case when the solvable Leibniz algebra is decomposed as a direct sum of its nilradical, which is a direct sum of null-filiform ideals and a one-dimensional complementary subspace. Moreover, in this case we establish that these ideals are ideals of the algebra as well.

On Evolution Algebras

The structural constants of an evolution algebra is given by a quadratic matrix

Universal Strict General Actors and Actors in Categories of Interest

A

Crossed modules and homology

. In this work we establish equivalence between nil, right nilpotent evolution algebras and evolution algebras, which are defined by upper triangular matrix

On Solvability and Nilpotency of Leibniz n-Algebras

A

The actor of a crossed module in lie algebras

. The classification of 2-dimensional complex evolution algebras is obtained. For an evolution algebra with a special form of the matrix

ON NILPOTENT LEIBNIZ n-ALGEBRAS

A

Crossed modules for Leibniz n-algebras

we describe all its isomorphisms and their compositions. We construct an algorithm running under Mathematica which decides if two finite dimensional evolution algebras are isomorphic.

CYCLIC HOMOLOGIES OF CROSSED MODULES OF ALGEBRAS

For any category of interest ℂ we define a general category of groups with operations

Left-right noncommutative Poisson algebras

\mathbb{C_G}, \mathbb{C}\hookrightarrow\mathbb{C_G}