1,720,974 research outputs found
Root involutions, real forms and diagrams
No full textWe study the correspondence between equivalence classes of pairs consisting of real semisimple Lie algebras and their Cartan subalgebras and involutions of the corresponding root system. This can be graphically described by introducing S- and Sigma- diagrams , generalizing those of Satake and Vogan. (c) 2024 The Author(s). Published by Elsevier GmbH. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)
Spoleto e il suo territorio: il centro storico, la Rocca albornoziana, Monteluco (lecceta primigenia). Centri storici minori dello Spoletino: i castelli di Eggi e S. Giacomo di Spoleto (case-torri-palombaie).
No full textOn some classes of Z -graded Lie algebras
No full textWe study finite dimensional almost- and quasi-effective prolongations of nilpotent Z-graded Lie algebras, especially focusing on those having a decomposable reductive structural subalgebra. Our assumptions generalize effectiveness and algebraicity and are appropriate to obtain Levi–Malčev and Levi–Chevalley decompositions and precisions on the heigth and other properties of the prolongations in a very natural way. In a last section we consider the semisimple case and discuss some examples in which the structural algebras are central extensions of orthogonal Lie algebras and their degree (-1) components arise from spin representations
Higher order Levi forms on homogeneous CR manifolds
Full text linkWe investigate the nondegeneracy of higher order Levi forms on weakly nondegenerate homogeneous CR manifolds. Improving previous results, we prove that general orbits of real forms in complex flag manifolds have order less or equal than 3 and the compact ones less or equal 2. Finally we construct by Lie extensions weakly nondegenerate CR vector bundles with arbitrary orders of nondegeneracy
On finitely nondegenerate closed homogeneous CR manifolds
No full textA complex flag manifold F=G/Q decomposes into finitely many real orbits under the action of a real form G(s) of G. Their embedding into F defines on them CR manifold structures. We characterize and list all the closed real orbits which are finitely nondegenerate
Algebras of infinitesimal CR automorphisms
No full textThis paper is devoted to the investigation of Lie algebras of local infinitesimal CR automorphisms. Such algebras are naturally associated to germs of homogeneous CR manifolds. The authors introduce a corresponding abstract notion of CR algebra. A CR algebra is a pair (L,L1), consisting of a real Lie algebra L and a subalgebra L1 of the complexification C⊗RL, such that the factor space L/L∩L1 is finite-dimensional.
The authors investigate some formal properties of CR algebras and construct some "fibrations'' (i.e., L-equivariant submersions) of such algebras. They introduce three new notions of nondegeneracy of CR algebras---strict, weak and ideal nondegeneracy. These three concepts are weaker than those used previously by some other authors. The authors intend to extend the application of the É. Cartan method of investigating the equivalence of CR structures to some larger classes of CR manifolds.
One of the main ideas of this paper is a decomposition of arbitrary CR algebras into three "parts'': totally real, totally complex and weakly nondegenerate CR algebras (Theorems 5.3 and 5.4). There are some results about these three special classes of CR algebras. Some results about prolongations for transitive CR algebras are also obtained, in particular about maximality of parabolic CR algebras with respect to transitive prolongations
On transitive contact and CR algebras
Full text linkWe consider locally homogeneous CR manifolds and show that, under a condition only depending on their underlying contact structure, their CR automorphisms form a finite dimensional Lie group
La Valle del Tescio. Lineamenti Geografici
No full textIl F. Tescio , tributario in sinistra del F. Chiascio (bacino del F. Tevere), scorre da est verso ovest con una lunghezza media dell’asta principale di circa 20km e sottende un bacino con un’area di 66km2 e un perimetro di 43km circa.
La quota massima è di 1.290m (M. Subasio), la minima di 197m alla confluenza con il F. Tevere.
Le caratteristiche morfometriche e morfologiche del bacino idrografico del F. Tescio sono il risultato delle interazioni tra processi morfogenetici fluviali e gravitativi (solo localmente intervengono processi antropici e legati a morfogenesi carsica) e fattori strutturali (litotipi affioranti, assetto strutturale, discontinuità principali e secondarie, caratteristiche geomeccaniche)
Families of Almost Complex Structures and Transverse (p, p)-Forms
No full textAnalmost p-Kahler manifold is a triple (M, J, Omega), where (M, J) is an almost complex manifold of real dimension 2n and Omega is a closed real transverse (p, p)-form on (M, J), where 1 <= p <= n. When J is integrable, almost p-Kahler manifolds are called p-Kahler manifolds. We produce families of almost p-Kahler structures (J(t), Omega(t)) on C-3, C-4, and on the real torus T-6, arising as deformations of Kahler structures (J(0), g(0), omega(0)), such that the almost complex structures Jt cannot be locally compatible with any symplectic form for t not equal 0. Furthermore, examples of special compact nilmanifolds with and without almost p-Kahler structures are presented
On the topology of minimal orbits in complex flag manifolds
No full textWe compute the Euler-Poincare characteristic of the homogeneous compact manifolds that can be described as minimal orbits for the action of a real form in a complex flag manifold
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