Antonio J. Calderón Martín

On Simple Split Lie Triple Systems

It is shown that simple split Lie triple systems with a coherent 0-root space and satisfying finiteness conditions are isomorphic to a direct limit of (well-known) finite dimensional simple Lie triple systems of a same type. The key tool in this job is the notion of connection of roots in the framework of split Lie triple systems.

On split Lie triple systems II

AbstractWe begin the study of arbitrary split Lie triple systems by focussing on those with a coherent 0-root space. We show that any such triple systems T with a symmetric root system is of the form T =

On graded matrix Hom-algebras

\mathcal{U}

Leibniz Algebras Admitting a Multiplicative Basis

+ ΜjIj with

Modules over linear spaces admitting a multiplicative basis

\mathcal{U}

ANTI)COMMUTATIVE ALGEBRAS WITH A MULTIPLICATIVE BASIS

a subspace of the 0-root space T0 and any Ij a well described ideal of T, satisfying [Ij, T, Ik] = 0 if j ≠ k. Under certain conditions, it is shown that T is the direct sum of the family of its minimal ideals, each one being a simple split Lie triple system, and the simplicity of T is characterized. The key tool in this job is the notion of connection of roots in the framework of split Lie triple systems.