Elliptic operators and Lie groups

Author: Derek W. Robinson

Publisher: Oxford University Press, USA


Category: Mathematics

Page: 558

View: 6566


Elliptic operators arise naturally in several different mathematical settings, notably in the representation theory of Lie groups, the study of evolution equations, and the examination of Riemannian manifolds. This book develops the basic theory of elliptic operators on Lie groups and thereby extends the conventional theory of parabolic evolution equations to a natural noncommutative context. In order to achieve this goal, the author presents a synthesis of ideas from partial differential equations, harmonic analysis, functional analysis, and the theory of Lie groups. He begins by discussing the abstract theory of general operators with complex coefficients before concentrating on the central case of second-order operators with real coefficients. A full discussion of second-order subelliptic operators is also given. Prerequisites are a familiarity with basic semigroup theory, the elementary theory of Lie groups, and a firm grounding in functional analysis as might be gained from the first year of a graduate course.

Quantum and Non-Commutative Analysis

Past, Present and Future Perspectives

Author: Huzihiro Araki,Keiichi R. Ito,Akitaka Kishimoto,Izumi Ojima

Publisher: Springer Science & Business Media

ISBN: 9401728232

Category: Science

Page: 464

View: 846


In the past decade, there has been a sudden and vigorous development in a number of research areas in mathematics and mathematical physics, such as theory of operator algebras, knot theory, theory of manifolds, infinite dimensional Lie algebras and quantum groups (as a new topics), etc. on the side of mathematics, quantum field theory and statistical mechanics on the side of mathematical physics. The new development is characterized by very strong relations and interactions between different research areas which were hitherto considered as remotely related. Focussing on these new developments in mathematical physics and theory of operator algebras, the International Oji Seminar on Quantum Analysis was held at the Kansai Seminar House, Kyoto, JAPAN during June 25-29, 1992 by a generous sponsorship of the Japan Society for the Promotion of Science and the Fujihara Foundation of Science, as a workshop of relatively small number of (about 50) invited participants. This was followed by an open Symposium at RIMS, described below by its organizer, A. Kishimoto. The Oji Seminar began with two key-note addresses, one by V.F.R. Jones on Spin Models in Knot Theory and von Neumann Algebras and by A. Jaffe on Where Quantum Field Theory Has Led. Subsequently topics such as Subfactors and Sector Theory, Solvable Models of Statistical Mechanics, Quantum Field Theory, Quantum Groups, and Renormalization Group Ap proach, are discussed. Towards the end, a panel discussion on Where Should Quantum Analysis Go? was held.

Algebraic Groups and Lie Groups

A Volume of Papers in Honour of the Late R. W. Richardson

Author: T. A. Springer,Roger Wolcott Richardson,G. I. Lehrer,Alan L. Carey,Michael Murray

Publisher: Cambridge University Press

ISBN: 9780521585323

Category: Mathematics

Page: 384

View: 9569


This volume is a unique and comprehensive collection of works by some of the world's leading researchers. Papers on algebraic geometry, algebraic groups, and Lie groups are woven together to form a connection between the study of symmetry and certain algebraic structures. This connection reflects the interests of R. W. Richardson who studied the links between representation theory and the structure and geometry of algebraic groups. In particular, the papers address Kazhdan-Lusztig theory, quantum groups, spherical varieties, symmetric varieties, cohomology of varieties, purity, Schubert geometry, invariant theory and symmetry breaking. For those working on algebraic and Lie groups, this book will be a wealth of fascinating material.

Evolution Equations and Their Applications in Physical and Life Sciences

Author: G Lumer

Publisher: CRC Press

ISBN: 1482277484

Category: Medical

Page: 532

View: 430


This volume presents a collection of lectures on linear partial differntial equations and semigroups, nonlinear equations, stochastic evolutionary processes, and evolution problems from physics, engineering and mathematical biology. The contributions come from the 6th International Conference on Evolution Equations and Their Applications in Physica