A. J. Calderón Martín

On Integrable roots in split Lie triple systems

We focus on the notion of an integrable root in the framework of split Lie triple systems T with a coherent 0-root space. As a main result, it is shown that if T has all its nonzero roots integrable, then its standard embedding is a split Lie algebra having all its nonzero roots integrable. As a consequence, a local finiteness theorem for split Lie triple systems, saying that whenever all nonzero roots of T are integrable then T is locally finite, is stated. Finally, a classification theorem for split simple Lie triple systems having all its nonzero roots integrable is given.

Associative Algebras Admitting a Quasi-multiplicative Basis

A basis ℬ={ei}i∈I

On Locally Finite Split Lie Triple Systems

{\mathcal B}=\{e_{i}\}_{i \in I}

The banach-lie group of lie triple automorphisms of an H*-algebra

of an associative algebra A,

Split Twisted Inner Derivation Triple Systems

{\frak A},

Hilbert space methods in the theory of Lie triple systems

over an arbitrary base field 𝔽

On involutive Lie algebras having a Cartan decomposition

{\mathbb F}

A characterization of the semisimplity of Lie-type algebras through the existence of certain linear bases

, is called multiplicative if for any i,j∈I we have that eiej∈𝔽ek

The classification of N-dimensional non-Lie Malcev algebras with (N-4)-dimensional annihilator

e_{i}e_{j} \in {\mathbb F} e_{k}

INHERITANCE OF PRIMENESS BY IDEALS IN LIE TRIPLE SYSTEMS

for some k∈I. The class of associative algebras admitting a multiplicative basis can be seen as a particular case of the more general class of associative algebras admitting a quasi-multiplicative basis. In the present paper we prove that if an associative algebra A