Sugawara Operators for Classical Lie Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Sugawara Operators for Classical Lie Algebras write by Alexander Molev:. This book was released on 2018-02-28. Sugawara Operators for Classical Lie Algebras available in PDF, EPUB and Kindle. The celebrated Schur-Weyl duality gives rise to effective ways of constructing invariant polynomials on the classical Lie algebras. The emergence of the theory of quantum groups in the 1980s brought up special matrix techniques which allowed one to extend these constructions beyond polynomial invariants and produce new families of Casimir elements for finite-dimensional Lie algebras. Sugawara operators are analogs of Casimir elements for the affine Kac-Moody algebras. The goal of this book is to describe algebraic structures associated with the affine Lie algebras, including affine vertex algebras, Yangians, and classical -algebras, which have numerous ties with many areas of mathematics and mathematical physics, including modular forms, conformal field theory, and soliton equations. An affine version of the matrix technique is developed and used to explain the elegant constructions of Sugawara operators, which appeared in the last decade. An affine analogue of the Harish-Chandra isomorphism connects the Sugawara operators with the classical -algebras, which play the role of the Weyl group invariants in the finite-dimensional theory.
Lie Algebras of Bounded Operators
Lie Algebras of Bounded Operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lie Algebras of Bounded Operators write by Daniel Beltita. This book was released on 2012-12-06. Lie Algebras of Bounded Operators available in PDF, EPUB and Kindle. In several proofs from the theory of finite-dimensional Lie algebras, an essential contribution comes from the Jordan canonical structure of linear maps acting on finite-dimensional vector spaces. On the other hand, there exist classical results concerning Lie algebras which advise us to use infinite-dimensional vector spaces as well. For example, the classical Lie Theorem asserts that all finite-dimensional irreducible representations of solvable Lie algebras are one-dimensional. Hence, from this point of view, the solvable Lie algebras cannot be distinguished from one another, that is, they cannot be classified. Even this example alone urges the infinite-dimensional vector spaces to appear on the stage. But the structure of linear maps on such a space is too little understood; for these linear maps one cannot speak about something like the Jordan canonical structure of matrices. Fortunately there exists a large class of linear maps on vector spaces of arbi trary dimension, having some common features with the matrices. We mean the bounded linear operators on a complex Banach space. Certain types of bounded operators (such as the Dunford spectral, Foia§ decomposable, scalar generalized or Colojoara spectral generalized operators) actually even enjoy a kind of Jordan decomposition theorem. One of the aims of the present book is to expound the most important results obtained until now by using bounded operators in the study of Lie algebras.
Mappings of Operator Algebras
Mappings of Operator Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mappings of Operator Algebras write by H. Araki. This book was released on 2012-12-06. Mappings of Operator Algebras available in PDF, EPUB and Kindle. This volume consists of articles contributed by participants at the fourth Ja pan-U.S. Joint Seminar on Operator Algebras. The seminar took place at the University of Pennsylvania from May 23 through May 27, 1988 under the auspices of the Mathematics Department. It was sponsored and supported by the Japan Society for the Promotion of Science and the National Science Foundation (USA). This sponsorship and support is acknowledged with gratitude. The seminar was devoted to discussions and lectures on results and prob lems concerning mappings of operator algebras (C*-and von Neumann alge bras). Among the articles contained in these proceedings, there are papers dealing with actions of groups on C* algebras, completely bounded mappings, index and subfactor theory, and derivations of operator algebras. The seminar was held in honor of the sixtieth birthday of Sh6ichir6 Sakai, one of the great leaders of Functional Analysis for many decades. This vol ume is dedicated to Professor Sakai, on the occasion of that birthday, with the respect and admiration of all the contributors and the participants at the seminar. H. Araki Kyoto, Japan R. Kadison Philadelphia, Pennsylvania, USA Contents Preface.... ..... ....... ........... ...... ......... ................ ...... ............... ... vii On Convex Combinations of Unitary Operators in C*-Algebras UFFE HAAGERUP ......................................................................... .
Basic Irreducible Modules of the Classical Lie Algebras
Basic Irreducible Modules of the Classical Lie Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Basic Irreducible Modules of the Classical Lie Algebras write by Elaine Roberta Glickman. This book was released on 1965. Basic Irreducible Modules of the Classical Lie Algebras available in PDF, EPUB and Kindle.
Lie algebras of unbounded operators
Lie algebras of unbounded operators - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lie algebras of unbounded operators write by Palle E. T. Jørgensen. This book was released on 1980. Lie algebras of unbounded operators available in PDF, EPUB and Kindle.
