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41.
Fangyan Lu 《Journal of Functional Analysis》2006,240(1):84-104
A Lie isomorphism ? between algebras is called trivial if ?=ψ+τ, where ψ is an (algebraic) isomorphism or a negative of an (algebraic) anti-isomorphism, and τ is a linear map with image in the center vanishing on each commutator. In this paper, we investigate the conditions for the triviality of Lie isomorphisms from reflexive algebras with completely distributive and commutative lattices (CDCSL). In particular, we prove that a Lie isomorphism between irreducible CDCSL algebras is trivial if and only if it preserves I-idempotent operators (the sum of an idempotent and a scalar multiple of the identity) in both directions. We also prove the triviality of each Lie isomorphism from a CDCSL algebra onto a CSL algebra which has a comparable invariant projection with rank and corank not one. Some examples of Lie isomorphisms are presented to show the sharpness of the conditions. 相似文献
42.
E. Horozov 《Bulletin des Sciences Mathématiques》2002,126(7):605-614
In this paper we give another characterization of the strictly nilpotent elements in the Weyl algebra, which (apart from the polynomials) turn out to be all bispectral operators with polynomial coefficients. This also allows to reformulate in terms of bispectral operators the famous conjecture, that all the endomorphisms of the Weyl algebra are automorphisms (Dixmier, Kirillov, etc). 相似文献
43.
Jorge Lauret 《Annals of Global Analysis and Geometry》2006,30(2):107-138
Let (N, γ) be a nilpotent Lie group endowed with an invariant geometric structure (cf. symplectic, complex, hypercomplex or any of their ‘almost’ versions). We define a left invariant Riemannian metric on N compatible with γ to be minimal, if it minimizes the norm of the invariant part of the Ricci tensor among all compatible metrics with the same scalar curvature. We prove that minimal metrics (if any) are unique up to isometry and scaling, they develop soliton solutions for the ‘invariant Ricci’ flow and are characterized as the critical points of a natural variational problem. The uniqueness allows us to distinguish two geometric structures with Riemannian data, giving rise to a great deal of invariants.Our approach proposes to vary Lie brackets rather than inner products; our tool is the moment map for the action of a reductive Lie group on the algebraic variety of all Lie algebras, which we show to coincide in this setting with the Ricci operator. This gives us the possibility to use strong results from geometric invariant theory.Communicated by: Nigel Hitchin (Oxford)
Mathematics Subject Classifications (2000): Primary: 53D05, 53D55; Secondary: 22E25, 53D20, 14L24, 53C30. 相似文献
45.
Daszkiewicz Andrzej Kraśkiewicz Witold Przebinda Tomasz 《Central European Journal of Mathematics》2005,3(3):430-474
We classify the homogeneous nilpotent orbits in certain Lie color algebras and specialize the results to the setting of a
real reductive dual pair.
For any member of a dual pair, we prove the bijectivity of the two Kostant-Sekiguchi maps by straightforward argument. For
a dual pair we determine the correspondence of the real orbits, the correspondence of the complex orbits and explain how these
two relations behave under the Kostant-Sekiguchi maps. In particular we prove that for a dual pair in the stable range there
is a Kostant-Sekiguchi map such that the conjecture formulated in [6] holds. We also show that the conjecture cannot be true
in general. 相似文献
46.
本文证明了下面主要结果:设G是n-可解群,π是一些素数之集,若对任意p∈∩π(G),(p,n(1-n))=1,则G的π-Hall子群的个数r=k1k2...kt,每ki≡1(modp),某P∈π,且每ki整除G的一个主因子。 相似文献
47.
B. A. Omirov 《Mathematical Notes》2005,77(5-6):677-685
The algebras of derivations of naturally graded Leibniz algebras are described. The existence of characteristically nilpotent Leibniz algebras in any dimension greater than 4 is proved.__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 733–742.Original Russian Text Copyright ©2005 by B. A. Omirov. 相似文献
48.
Viktor Ostrik 《Compositio Mathematica》2002,132(3):283-287
Let U be a quantumgroup with divid d powers at root ofunity constructed froma rootsystem R .Let u U b th small quantumgroup.Th cohomologyof u with trivial coefficients was computed by Ginzburg and Kumar.It turns out to be isomorphic to the functions algebra of the nilpotent cone of a semisimpl algebraic group with root system R .In this not we calculate cohomology of u with coefficients in simplest reducible tilting modul with nontrivial cohomology.It appears to b isomorphic to th functions algebra of th closure of the subregular nilpotent orbit. 相似文献
49.
李殿龙 《数学的实践与认识》2008,38(8):143-146
研究迷向子群的结构是有限域上典型群几何中的一个重要问题.刻画了3-幂零矩阵的Jordan标准型在GLn(F)共轭作用下的迷向子群的结构. 相似文献
50.
两类幂零的n-Lie代数 总被引:4,自引:1,他引:3
本文提出并构造了两类幂零的n-Lie代数:特征幂零的n-Lie代数与最大秩的幂零的n-Lie代数.证明了n-Lie代数是特征幂零的n-Lie代数的充分必要条件,以及最大秩的幂零的n-Lie代数的结构特征. 相似文献