NOT ASSOCIATIVE ALGEBRA

Author: PANIELLO ALSTRUEY IRENE.
Year: 2003.
University: ZARAGOZA [www.unizar.es].
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: This report addresses two aspects of the theory of structure of the systems of Jordan. In primerlugar, the study of systems of polynomial Jordan with identities, and then the theory delocalización of them. Among systems Jordan and Lie algebras, provides construction deKantor-Koecher-Tits.En what the study of systems with identities polynomial concerns, we will highlight the siguientesresultados: 1 .- The partnership pairs primitive version of the theorem Amitsur. 2 .- It shows, for pairs and triples systems Jordan, that any system of Jordan IP satisfaceuna identity polynomial homótopa.3 .- As a result, the test version of Lie algebras Jordan 3-graduadas's theorem dePosner Rowen for PI-álgebras primas.La second part of the report is devoted to the study of the theory of localization of algebra deJordan, with the aim of developing a more general theory in the sense constructions deJohnson and Martindale in the case of associations. This introduces a concept of algebra ratios queengloba both algebras classic ratios as central ratios. It also introduces lanoción of maximalidad for such algebra of quotients. Then, there are conditions queaseguren the existence of such algebras and gives a description of the mismas.Finalmente, moves the definition of algebra of quotients, road construction Kantor-Koecher-Tits, at Lie algebras. That is a notion of algebra of quotients and maximal algebra of quotients paraálgebras Lie graded by root systems of type A (1). In addition, using the resultadosobtenidos for algebras Jordan, is the description of the maximal algebra ratios talesálgebras.

Author: MARTÍN HERCE FABIÁN.
Year: 2005.
University: LA RIOJA [www.unirioja.es].
Place of defense: UNIVERSIDAD DE LA RIOJA.
Place of preparation: UNIVERSIDAD DE LA RIOJA.

Summary: One of the bridges that link geometry and algebra is given through the connection between the spaces homogeneous reductivos and algebras of Lie-Yamaguti (also known in the literature as a general Lie triple systems, or triple Lie algebras) . This thesis explores such algebras of Lie-Yamaguti, and, through the determination of descomposiciones reductivas of Lie algebras, it reaches a complete ranking of which appear to be irreducible natural as a module for its derivations on internal bodies algebra closed feature zero. The classification is very interesting, because for their achievement, are used as important tools a large number of non-associative structures well known (triple Lie, pairs of Jordan, constructions Tits) so that the algebra of Lie-Yamaguti obtained are blocks can organize in different types of systems.

Author: PÉREZ MARTÍN FRANCISCO DE PAULA.
Year: 2006.
University: SEVILLA [www.us.es].
Place of defense: E.T.S. DE INGENIERÍA INFORMÁTICA.
Place of preparation: E.T.S. DE INGENIERÍA INFORMÁTICA.

Summary: The aim of the thesis is to complete the classification, except isomorfismos from Álgebras Lie cuasifiliformes complex dimension 9. It proves that there are 5 families triparamétricas, 24 biparamétricas, 77 monoparamétricas and 157 algebras Lie, so that two algebras any of them are not isoforms between themselves and any Lie algebra dimension 9 cuasifiliforme is isomorfa to one of those found. Saying that the computational treatment plays an important role in this work is not only the obvious but even fall short. But somehow work out in "frontier regions", from the scientific point of view. On the one hand is at the limit of what can be classified comprehensively with computer aid and is also on the edge of what appears useful to classify them thoroughly. Probably what should be done from this point is to seek subfamilies, in a way, "representing" many others - for example, algebra course graduates.