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1.
本文我们用幂零李群表示的方法给出了二步幂零李群上一类左不变微分算子是亚椭圆的充要条件。 相似文献
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《数学的实践与认识》2018,(19)
3维Heisenberg群H_3是二阶幂零李群,是Thurston几何化猜想中几何结构的8种模型结构之一.主要从勒让德对偶的视角考察3维Heisenberg群上正则曲线的切球面指标线和副法球面指标线之间的对偶关系,发现了刻画副法球面指标线奇点的几何不变量. 相似文献
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Engel群是次黎曼几何中的一类重要的单连通幂零李群.本文研究了Engel群E=(R4,■,{δλ})的有界区域Ω上次Laplace算子△E的狄利克雷特征值问题■其中v是边界?Ω的单位外法向量场.我们建立了该问题的一些万有特征值不等式. 相似文献
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《数学的实践与认识》2017,(21)
3维Heisenberg群H_3是具有4维等距群的齐性流形,是除了空间形式之外最简单的3维流形之一,而且从代数观点来看,H_3是二阶幂零李群.主要从奇点理论的视角考察3维Heisenberg群上球面曲线的渐屈线的奇异性质,主要结果表明这类渐屈线可以被视作焦曲线并且局部上微分同胚于一般尖点. 相似文献
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零代数在什么条件下是幂零的?这是一个重要问题。类似地,我们提出另一问题,对于幂零元生成的子代数在什么条件下是幂零的?一个幂零元生成的子代数显然是幂零的,两个幂零元生成的子代数一般不是诣零的。本文得到一个肯定结果: 相似文献
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我们讨论了p-幂零限制李超代数的一些性质,分别给出了p-幂零和幂零限制李超代数的几个充分必要条件,并讨论了幂零与p-幂零之间的关系.最后,证明了幂零限制李超代数的一些性质. 相似文献
9.
幂等右侧Quantale上的幂零矩阵 总被引:2,自引:0,他引:2
讨论幂等右侧Quantale上的幂零矩阵的若干性质,给出了幂等右侧Quantale上的矩阵为幂零矩阵的充要条件,得到了幂零矩阵的幂零指数的刻画定理。 相似文献
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We generalize the classical Paley–Wiener theorem to special types of connected, simply connected, nilpotent Lie groups: First we consider nilpotent Lie groups whose Lie algebra admits an ideal which is a polarization for a dense subset of generic linear forms on the Lie algebra. Then we consider nilpotent Lie groups such that the co-adjoint orbits of all the elements of a dense subset of the dual of the Lie algebra 𝔤* are flat (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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S. G. Dani 《Transactions of the American Mathematical Society》2003,355(4):1491-1503
We construct examples of two-step and three-step nilpotent Lie groups whose automorphism groups are ``small' in the sense of either not having a dense orbit for the action on the Lie group, or being nilpotent (the latter being stronger). From the results we also get new examples of compact manifolds covered by two-step simply connected nilpotent Lie groups which do not admit Anosov automorphisms.
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This paper is devoted to a class of homogeneous left invariant operators L\ on the nilpotent Lie group G^{d+2} of the form
$L-\lambda=-\sum\limits_{j=1}^d X_j^2-i\sum\limits_{m=1}^2 \lambda _m T_m,\lambda=\lambda_1,\lambda_2)\in C^2$
where {X_1,\cdots ,X_d,T_1, T_2} is a base of left invariant vector fields on G^{d+2}. With aid of harmonic analysis on nilpotent Lie groups and the method of increment operators, for all admissible L_\lambda, subelliptic estimate and an explicit inverse axe given and the hypoellipticity and the global solvability are obtained. Also, the structure of the set of admissible points \lambda is described exhaustively. 相似文献
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Cynthia Will 《Monatshefte für Mathematik》2010,135(1):425-437
The only known examples of non-compact Einstein homogeneous spaces are standard solvmanifolds (special solvable Lie groups
endowed with a left invariant metric), and according to a long standing conjecture, they might be all. The classification
of Einstein solvmanifolds is equivalent to the one of Einstein nilradicals, i.e. nilpotent Lie algebras which are nilradicals of the Lie algebras of Einstein solvmanifolds. Up to now, very few examples
of
\mathbb N{\mathbb N}-graded nilpotent Lie algebras that cannot be Einstein nilradicals have been found. In particular, in each dimension, there
are only finitely many known. We exhibit in the present paper two curves of pairwise non-isomorphic nine-dimensional two-step
nilpotent Lie algebras which are not Einstein nilradicals. 相似文献
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In this paper, we construct two-step nilpotent Lie groups from homogeneous fiber bundles over compact symmetric spaces. The structure of the constructed nilpotent groups is expressed in terms of the compact Lie groups involved in the fiber bundles. There are close relations between the geometric properties of the nilpotent groups and the total spaces of the fiber bundles. We will find new examples of nilpotent groups which are weakly symmetric and Riemannian geodesic orbit spaces. 相似文献
16.
S. K. Ray 《Proceedings Mathematical Sciences》2001,111(3):293-318
We extend an uncertainty principle due to Cowling and Price to two step nilpotent Lie groups, which generalizes a classical
theorem of Hardy. We also prove an analogue of Heisenberg inequality on two step nilpotent Lie groups. 相似文献
17.
Cynthia Will 《Monatshefte für Mathematik》2010,159(4):425-437
The only known examples of non-compact Einstein homogeneous spaces are standard solvmanifolds (special solvable Lie groups endowed with a left invariant metric), and according to a long standing conjecture, they might be all. The classification of Einstein solvmanifolds is equivalent to the one of Einstein nilradicals, i.e. nilpotent Lie algebras which are nilradicals of the Lie algebras of Einstein solvmanifolds. Up to now, very few examples of ${\mathbb N}$ -graded nilpotent Lie algebras that cannot be Einstein nilradicals have been found. In particular, in each dimension, there are only finitely many known. We exhibit in the present paper two curves of pairwise non-isomorphic nine-dimensional two-step nilpotent Lie algebras which are not Einstein nilradicals. 相似文献
18.
Spectral Properties of Second Order Differential Operators on Two-step Nilpotent Lie Groups
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In this paper, spectral properties of certain left invariant differential operators on two-step nilpotent Lie groups are completely described by using the theory of unitary irreducible representations and the Plancherel formulae on nilpotent Lie groups. 相似文献
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L. Magnin 《Algebras and Representation Theory》2010,13(6):723-753
For any complex 6-dimensional nilpotent Lie algebra
\mathfrakg,\mathfrak{g}, we compute the strain of all indecomposable 7-dimensional nilpotent Lie algebras which contain
\mathfrakg\mathfrak{g} by the adjoining a derivation method. We get a new determination of all 7-dimensional complex nilpotent Lie algebras, allowing
to check earlier results (some contain errors), along with a cross table intertwining nilpotent 6- and 7-dimensional Lie algebras. 相似文献
20.
V. A. Roman′kov 《Siberian Mathematical Journal》2016,57(4):679-695
We determine the exact values of the commutator width of absolutely free and free solvable Lie rings of finite rank, as well as free and free solvable Lie algebras of finite rank over an arbitrary field. We calculate the values of the commutator width of free nilpotent and free metabelian nilpotent Lie algebras of rank 2 or of nilpotency class 2 over an arbitrary field. We also find the values of the commutator width for free nilpotent and free metabelian nilpotent Lie algebras of finite rank at least 3 over an arbitrary field in the case that the nilpotency class exceeds the rank at least by 2. In the case of free nilpotent and free metabelian nilpotent Lie rings of arbitrary finite rank, as well as free nilpotent and free metabelian nilpotent Lie algebras of arbitrary finite rank over the field of rationals, we calculate the values of commutator width without any restrictions. It follows in particular that the free or nonabelian free solvable Lie rings of distinct finite ranks, as well as the free or nonabelian free solvable Lie algebras of distinct finite ranks over an arbitrary field are not elementarily equivalent to each other. We also calculate the exact values of the commutator width of free ?-power nilpotent, free nilpotent, free metabelian, and free metabelian nilpotent groups of finite rank. 相似文献