LIE ALGEBRA

Author: FALCÓN GANFORNINA RAÚL MANUEL.
Year: 2004.
University: SEVILLA [www.us.es].
Place of defense: FACULTAD DE MATEMÁTICAS.
Place of preparation: FACULTAD DE MATEMÁTICAS.

Summary: The Report submitted question on the extent of Isoteoría of Santilli varieties distinguishable and Lie groups. The Isoterapia is essentially to extend the concept of unity to an operator who depends on external factors and that, in their case, can be non-linear and non hamiltoniano. It opens this new form of unity stretch (lifting) traditional theories of mathematics: algebra analysis, geometry, etc.. The thesis before us are introduced in the first place the tools necessary to get the extension, ie isotopic lifting of Lie groups, making use of model construction isoproducto based on the multiplication, introduced in earlier work by the author of the same, the construction of which is the ultimate goal of this thesis. To that end, previously should extend the differential calculus and varieties distinguishable, leading respectively to calculate isodifernecial and isovariedades isodiferenciables. To carry out such constructions that makes use of the so-called "isotopías of Santilli", in particular those obtained from a isounidad I of an operation. The report is divided into 5 chapters. The first definitions are presented and the results are already known more important isoteoría. In the following three chapters examine extensions euclidea geometry, differential calculus and differential varieties, respectively, with a view to their subsequent use in lifting Lie Groups. Finally, the last chapter of the thesis is devoted to the construction of isogrupos isotopic and Lie groups isotransformaciones, main objective of the same.

Author: FALCÓN GANFORNINA RAÚL MANUEL.
Year: 2004.
University: SEVILLA [www.us.es].
Place of defense: FACULTAD DE MATEMÁTICAS.
Place of preparation: FACULTAD DE MATEMÁTICAS.

Summary: The Report submitted question on the extent of Isoteoría of Santilli varieties distinguishable and Lie groups. The Isoteoría is essentially to extend the concept of unity to an operator who depends on external factors and that, in their case, can be non-linear and non hamiltoniano. On this new form of unity stretch (lifting) traditional theories of mathematics: algebra, analysis, geometry, etc.. The thesis before us are introduced in the first place the tools necessary to get the extension, ie, lifting isotopic Lie groups, making use of model construction isoproducto based on the multiplication, introduced in earlier work by the author of the same, the construction of which is the ultimate goal of this thesis. To that end, previously should extend the differential calculus and varieties distinguishable, leading respectively to calculate isodiferencial and isovariedades isodiferenciables. To carry out such constructions that makes use of the so-called "isotopías of Santilli", in particular those obtained from a isounidad à and an operation *. The report is divided into 5 chapters. The first definitions are presented and the results are already known more important isoteoría. In the following three chapters examine extensions euclídea geometry, calculus and differential varieties distinguishable respectively, with a view to their subsequent use in lifting Lie Groups. Finally, the last chapter of the thesis is devoted to the construction of isogrupos isotopic and Lie groups isotransformaciones, main objective of the same.