A Pseudo-differential Calculus on Graded Nilpotent Lie Groups
نویسنده
چکیده
In this paper, we present first results of our investigation regarding symbolic pseudo-differential calculi on nilpotent Lie groups. On any graded Lie group, we define classes of symbols using difference operators. The operators are obtained from these symbols via the natural quantisation given by the representation theory. They form an algebra of operators which shares many properties with the usual Hörmander calculus.
منابع مشابه
Lévy Processes in a Step 3 Nilpotent Lie Group
The infinitesimal generators of Lévy processes in Euclidean space are pseudo-differential operators with symbols given by the Lévy-Khintchine formula. This classical analysis relies heavily on Fourier analysis which in the case when the state space is a Lie group becomes much more subtle. Still the notion of pseudo-differential operators can be extended to connected, simply connected nilpotent ...
متن کاملStatement of Research Interest
My research lies in the intersection of three fields of mathematics: stochastic processes, representation theory and the theory of Lie groups; in particular, Lévy processes in nilpotent Lie groups. In Euclidean space, these processes are generated by a particularly nice class of operator, referred to as a pseudo-differential operator. These operators have traditionally been of interest in the s...
متن کاملArithmetic Deformation Theory of Lie Algebras
This paper is devoted to deformation theory of graded Lie algebras over Z or Zl with finite dimensional graded pieces. Such deformation problems naturally appear in number theory. In the first part of the paper, we use Schlessinger criteria for functors on Artinian local rings in order to obtain universal deformation rings for deformations of graded Lie algebras and their graded representations...
متن کاملThe Large Scale Geometry of Nilpotent Lie Groups
In this paper, we prove results concerning the large scale geometry of connected, simply connected nilpotent Lie groups equipped with left invariant Riemannian metrics. Precisely, we prove that there do not exist quasi-isometric embeddings of such a nilpotent Lie group into either a CAT0 metric space or an Alexandrov metric space. The main technical aspect of this work is the proof of a limited...
متن کاملA Nilpotent Quotient Algorithm for Graded Lie Rings
A nilpotent quotient algorithm for graded Lie rings of prime characteristic is described. The algorithm has been implemented and applications have been made to the investigation of the associated Lie rings of Burnside groups. New results about Lie rings and Burnside groups are presented. These include detailed information on groups of exponent 5 and 7 and their associated Lie rings. Appeared: J...
متن کامل