COMMUTATIVE ALGEBRAS IN DRINFELD CATEGORIES OF ABELIAN LIE ALGEBRAS

We describe (braided-) commutative algebras with non-degenerate multiplicative form in certain braided monoidal categories, corresponding to abelian metric Lie algebras (so-called Drinfeld categories). We also describe local modules over these algebras and classify commutative algebras with a finite number of simple local modules.

Maximal Subgroups of Compact Lie Groups

This report aims at giving a general overview on the classification of the maximal subgroups of compact Lie groups (not necessarily connected). In the first part, it is shown that these fall naturally into three types: (1) those of trivial type, which are simply defined as inverse images of maximal subgroups of the corresponding component group under the canonical projection and whose classification constitutes a problem in finite group theory, (2) those of normal type, whose connected one-component is a normal subgroup, and (3) those of normalizer type, which are the normalizers of their own connected one-component. It is also shown how to reduce the classification of maximal subgroups of the last two types to: (2) the classification of the finite maximal Sigma-invariant subgroups of centerfree connected compact simple Lie groups and (3) the classification of the Sigma-primitive subalgebras of compact simple Lie algebras, where Sigma is a subgroup of the corresponding outer automorphism group. In the second part, we explicitly compute the normalizers of the primitive subalgebras of the compact classical Lie algebras (in the corresponding classical groups), thus arriving at the complete classification of all (non-discrete) maximal subgroups of the compact classical Lie groups.

On simple Lie algebras over a field of characteristic 2

We prove that the simple Lie algebras constructed by G. Jurman (2004) in 121 are isomorphic to Hamiltonian algebras. As a corollary we answer all questions formulated in G. Jurman (2004) [2] about isomorphisms of these algebras. (C) 2012 Elsevier Inc. All rights reserved.

Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence

We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized by the time variable t) of the velocity fluctuations to equip an affine space K3 of the correlation vectors by a family of metrics. It was shown in Grebenev and Oberlack (J Nonlinear Math Phys 18:109–120, 2011) that a special form of this tensor field generates the so-called semi-reducible pseudo-Riemannian metrics ds2(t) in K3. This construction presents the template for embedding the couple (K3, ds2(t)) into the Euclidean space R3 with the standard metric. This allows to introduce into the consideration the function of length between the fluid particles, and the accompanying important problem to address is to find out which transformations leave the statistic of length to be invariant that presents a basic interest of the paper. Also we classify the geometry of the particles configuration at least locally for a positive Gaussian curvature of this configuration and comment the case of a negative Gaussian curvature.

El clima en el Atlántico norafricano durante los interglaciales MIS 5.5 y MIS 11.3 a partir de los paleoindicadores Harpa rosea Lamarck [1816] y Saccaostrea cucullata (Born, 1780) en el archipiélago canario

Universidad de Las Palmas de Gran Canaria. Departamento de Biología. Programa de doctorado de Gestión de recursos vivos marinos y medioambiente ; bienio 2006-2008

Gran hidráulica y ocupación de la geografía árida de Norteamérica: una aproximación histórica, 1860-1960

[ES] Este trabajo tiene como propósito realizar una primera aproximación al proceso histórico de ocupación de la geografía árida de Norteamérica (1860-1960) que integra la frontera norte de México con el sureste de los Estados Unidos. Se hace énfasis en el impacto general que en este proceso jugó la revolución industrial y tecno-científica que la acompañó y específicamente el papel desempeñado de la Gran Hidráulica en la explotación de los recursos hídricos a gran escala, habilitando el desarrollo productivo y social. Como parte del cambio histórico se expone también la emergencia de un moderno marco jurídico-institucional en torno al agua. Se cierra con la exposición de dos casos regionales para mostrar las crecientes rivalidades por los recursos hídricos ante sus nuevos usos modernos y su explotación intensiva, así como las diferentes modalidades de gestión resultantes y sus impactos en el largo plazo. [EN] This work aims to make a first approach to the historical process of occupation of the arid geography of North America (1860-1960) that integrates the northern border of Mexico with the southeast of the United States. Emphasis on the general impact that this process played the industrial and technoscientific revolution that accompanied it and specifically the role of the great hydraulic in the exploitation of large-scale water resources, enabling productive and social development. As part of the historic change is also the emergence of a modern legal- institutional framework around water. It closes with the exhibition of two regional cases to show the growing rivalries for water resources to its new modern uses and its intensive exploitation, as well as the different forms of management resulting and their impacts in the long term.