Classification of simple linearly compact Kantor triple systems over the complex numbers

Simple finite dimensional Kantor triple systems over the complex numbers are classified in terms of Satake diagrams. We prove that every simple and linearly compact Kantor triple system has finite dimension and give an explicit presentation of all the classical and exceptional systems.Comment: 46 pages, 3 tables; v2: Major revision of the introduction; v3: Final version to appear in Journal of Algebr

Super Jordan triple systems and Kantor triple systems

We introduce the notion of $\epsilon$-super Jordan triple systems(sJTS), a supersymmetric generalization of Jordan triple systems which includes them as well as the class of N=6 3-algebras as particular cases. The Tits-Kantor-Koecher construction for Kantor triple systems(KTS) and for $\epsilon$-super Jordan triple systems is established and thanks to it the problem of classifying simple linearly-compact KTS and sJTS is reduced to the classification of particular classes of automorphisms of 5-graded Lie algebras and 3-graded Lie superalgebras. We obtain the classification of simple linearly-compact KTS and the classification of finite-dimensional simple sJTS

Infinite Atomized Semilattices

We extend the theory of atomized semilattices to the infinite setting. We show that it is well-defined and that every semilattice is atomizable. We also study atom redundancy, focusing on complete and finitely generated semilattices and show that for finitely generated semilattices, atomizations consisting exclusively of non-redundant atoms always exist.Comment: 25 pages, 2 figure

Lie algebras and triple systems

This thesis is dedicated to the Tits-Kantor-Koecher (TKK) construction which establishes a bijective correspondence between unital Jordan algebras and shortly graded Lie algebras with Z-grading induced by an sl_2-triple. It is based on the observation that if g is a Lie algebra with a short Z-grading and f lies in g_1, then the formula ab=[[a,f],b] defines a structure of a Jordan algebra on g_{-1}. The TKK construction has been extended to Jordan triple systems and, more recently, to the so-called Kantor triple systems. These generalizations are studied in the thesis

Coenzyme Q(10) supplementation in infertile men with idiopathic asthenozoospermia: an open, uncontrolled pilot study.

OBJECTIVE: To clarify a potential therapeutic role of coenzyme Q(10) (CoQ(10)) in infertile men with idiopathic asthenozoospermia. DESIGN: Open, uncontrolled pilot study. PATIENT(S): Infertile men with idiopathic asthenozoospermia. INTERVENTION(S): CoQ(10) was administered orally; semen samples were collected at baseline and after 6 months of therapy. MAIN OUTCOME MEASURE (S): Semen kinetic parameters, including computer-assisted sperm data and CoQ(10) and phosphatidylcholine levels. RESULT(S): CoQ(10) levels increased significantly in seminal plasma and in sperm cells after treatment. Phosphatidylcholine levels also increased. A significant increase was also found in sperm cell motility as confirmed by computer-assisted analysis. A positive dependence (using the Cramer's index of association) was evident among the relative variations, baseline and after treatment, of seminal plasma or intracellular CoQ(10) content and computer-determined kinetic parameters. CONCLUSION(S): The exogenous administration of CoQ(10) may play a positive role in the treatment of asthenozoospermia. This is probably the result of its role in mitochondrial bioenergetics and its antioxidant properties