Nilpotent flows of S1-invariant Hamiltonian systems on 4-dimensional symplectic manifolds

We investigate S¹-invariant Hamiltonian systems on compact 4-dimensional symplectic manifolds with free symplectic action of a circle. We show that, in a rather general case, such systems generate ergodic flows of types (quasiperiodic and nilpotent) on their isoenergetic surfaces. We solve the problem of straightening of these flows. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 1, pp. 122–140, January, 1997.     

一类幂零矩阵幂零指标的特征

设(L, ,·)是一个incline. 本文给出了一个incline上幂零矩阵幂零指标的特征.其结果改进了文[4]中的相应结论.     

幂零Fuzzy矩阵的一些结论及幂零度的求法

本文给出计算幂零Fuzzy矩阵的幂零度的两个办法,同时给出一个有有向Hamilton路的有向图的一个充分条件.     

Nilpotent lattice-ordered groups

Translated from Matematicheskie Zametki, Vol. 45, No. 1, pp. 72–79, January, 1989.     

Nilpotent n-Lie Algebras

We find examples of nilpotent n-Lie algebras and prove n-Lie analogs of classical group theory and Lie algebra results. As an example we show that a nilpotent ideal I of class c in a n-Lie algebra A with A/I ² nilpotent of class d is nilpotent and find a bound on the class of A. We also find that some classical group theory and Lie algebra results do not hold in n-Lie algebras. In particular, non-nilpotent n-Lie algebras can admit a regular automorphism of order p, and the sum of nilpotent ideals need not be nilpotent.     

幂零Lie群上的不定性原理

设N是具有平方可积表示的幂零Lie群,是其Plancherel测度．本文将N上群Fourier变换矩阵化,并由此给出N上不定性原理的一种定量描述．此外,还对N上不定性原理的定性描述（简称QUP）作了讨论,结果显示出N上QUP与P（λ）的零点集之代数、几何性质的一些联系.     

Nilpotent fusion categories

In this paper we extend categorically the notion of a finite nilpotent group to fusion categories. To this end, we first analyze the trivial component of the universal grading of a fusion category C, and then introduce the upper central series of C. For fusion categories with commutative Grothendieck rings (e.g., braided fusion categories) we also introduce the lower central series. We study arithmetic and structural properties of nilpotent fusion categories, and apply our theory to modular categories and to semisimple Hopf algebras. In particular, we show that in the modular case the two central series are centralizers of each other in the sense of M. Müger.     

Nilpotent completely positive maps

We study the structure of nilpotent completely positive maps in terms of Choi-Kraus coefficients. We prove several inequalities, including certain majorization type inequalities for dimensions of kernels of powers of nilpotent completely positive maps.     

Hypoelliptic Heat Kernels on Nilpotent Lie Groups

We study property RD in terms of rapid decay of matrix coefficients. We give new formulations of property RD in terms of a L¹-integrability condition of a Banach representation. Combining this new definition with the existence of cyclic subgroups of exponential growth in non-uniform lattices in semisimple Lie groups, we deduce that there exist matrix coefficients associated to several kinds of quasi-regular representations which satisfy a “non-RD condition” for non-uniform lattices. We obtain also that such coefficients can not satisfy the weak inequality of Harish-Chandra.     

Conjugate Points on 2-Step Nilpotent Groups

Let N be a simply connected 2-step nilpotent Lie group equipped with a left-invariant metric. We consider the characterizations of Jacobi fields and conjugate points along geodesics emanating from the identity element in N. We obtain a partial result for N and the complete result for N with a one-dimensional center.     

Nilpotent pseudogroups of functions on an interval

A near-identity nilpotent pseudogroup of order m 1 is a family f ₁, . . . , f _n : (-1, 1) of C ² functions for which: for some small positive real number < 1/10 ^m+1 and commutators of the functions f _i of order at least m equal the identity. We present a classification of near-identity nilpotent pseudogroups: our results are similar to those of Plante, Thurston, Farb and Franks. As an application, we classify certain foliations of nilpotent manifolds.     

Selfdecomposable Measures on Simply Connected Nilpotent Groups

The concepts of class L measures and selfdecomposable measures are generalised from vector spaces to simply connected nilpotent groups G. It has been shown that any full class L (probability) measure on G can be decomposed as = ₁* ... * _n, where each _i is a selfdecomposable measure on a subgroup G _i; itself is selfdecomposable under certain additional conditions—for example, when is symmetric. This generalizes a well known result on vector spaces. Some examples of class L measures on G are also constructed.     

Factorization of Periodic Locally Solvable Groups by Locally Nilpotent and Nilpotent Subgroups

We establish a series of new results concerning periodic locally solvable and finite solvable groups G = AB with locally nilpotent or nilpotent subgroups A and B.     

Filtering on manifolds

We coasider a partially observable diffusion process (x _t,y_t)t0 whose unobservable componentx _t lives on a submanifold M ofR ⁿ . We present some general conditions under which the conditional law ofx _t, given the observationsy _s ,s [0,t], admits a density w.r.t. a given measure on M. We characterize the analytical properties of this density by using appropriate Sobolev spaces.Research supported by the Hungarian National Foundation of Scientific Research No. 2290.     

Nets on manifolds

This paper is devoted to investigations on the geometry of multidimensional nets, connected with the thoery of distributions on smooth manifolds, and to the survey of some other papers on multidimensional nets, reviewed in RZh Matematika from 1964 to the present time.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 12, pp. 97–126, 1981.