一类幂零群上的特征值问题及估计

本文对幂零Lie群H_n×R^k上的Laplace算子,利用酉表示理论证明了它在全空间上无特征值存在,通过推广Friedrichs方法证明了在有界域上存在一列离散特征值,最后通过建立不变向量场之间的关系给出了特征值之差的估计.     

The Jacobson and Brown—McCoy Radicals of Certain Group Rings

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Metrics and tangent cones of uniformly regular Carnot—Carathéodory spaces

Given a uniformly regular Carnot—Carathéodory space, we prove equivalence of the quasimetrics generated by various bases of vector fields which agree with filtration of the space. We prove a theorem on a nilpotent tangent cone for a uniformly regular Carnot—Carathéodory space furnished with quasimetrics. As a consequence, we obtain a theorem on isomorphism of nilpotent tangent cones defined at a common distinguished point.     

Kernel of locally nilpotent

In this paper we study the kernel of a non-zero locally nilpotent -derivation of the polynomial ring over a noetherian integral domain containing a field of characteristic zero. We show that if is normal then the kernel has a graded -algebra structure isomorphic to the symbolic Rees algebra of an unmixed ideal of height one in , and, conversely, the symbolic Rees algebra of any unmixed height one ideal in can be embedded in as the kernel of a locally nilpotent -derivation of . We also give a necessary and sufficient criterion for the kernel to be a polynomial ring in general.

     

On Some Varieties of Soluble Lie Algebras

In this paper,we study a class of soluble Lie algebras with variety relations that the commutator of m and n is zero.The aim of the paper is to consider the relationship between the Lie algebra L with ...     

s-Stable Laws in Insurance and Finance and Generalization to Nilpotent Lie Groups

s-stable laws on Hilbert spaces, associated with some nonlinear transformations, were introduced by Jurek.^{(16, 18)} Here, we interpret certain s-stable motions as limits of total amount of claims processes (up to a deterministic reserve) of a portfolio of (nontraded) excess-of-loss reinsurance contracts and show that they lead to Erlang's model. We also give explicit formulas for the price of perpetual American options in case the logarithm of the price of the underlying asset is an s-stable motion. Furthermore, we generalize the concept of s-stability to simply connected nilpotent Lie groups. For step 2-nilpotent Lie groups we characterize the Lévy measure and the s-domain of attraction of nongaussian s-stable convolution semigroups.     

On the Simultaneous Triangulability of Matrices

Two necessary and sufficient criteria for the simultaneous triangulability of two complex matrices are established. Both of them admit a finite verification procedure. To prove the first criterion, classical theorems from Lie algebra theory are used, and known sufficient conditions of triangulability are also given a natural interpretation in terms of this theory. The other criterion is discussed in the framework of the associative algebras. Here the decisive fact is the Wedderburn theorem on the nilpotence of a finite-dimensional nilalgebra.     

The Fitting Subgroup and Some Injectors of Radical Locally Finite Groups with min-p for All p

Abstract

This work was intended as an attempt to continue the study of the class ? of generalised nilpotent groups started in a previous paper. We present some results concerning the Fitting subgroup and the ?-injectors of a radical locally finite group satisfying min-p for all p.