Representations of a Lie Algebra and Its Enveloping Algebra on Hilbert Space
Author: Bertram Kostant
Publisher:
Published: 1954
Total Pages: 194
ISBN-13:
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Author: Bertram Kostant
Publisher:
Published: 1954
Total Pages: 194
ISBN-13:
DOWNLOAD EBOOKAuthor: Konrad Schmüdgen
Publisher: Springer Nature
Published: 2020-07-28
Total Pages: 381
ISBN-13: 3030463664
DOWNLOAD EBOOKThis textbook provides an introduction to representations of general ∗-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers. The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of ∗-algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded ∗-algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensätze, induced representations, well-behaved representations and representations on rigged modules. Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference.
Author: H. Strade
Publisher: CRC Press
Published: 2020-08-11
Total Pages: 318
ISBN-13: 1000103390
DOWNLOAD EBOOKThis book presents an introduction to the structure and representation theory of modular Lie algebras over fields of positive characteristic. It introduces the beginner to the theory of modular Lie algebras and is meant to be a reference text for researchers.
Author: Jean-Philippe Anker
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 341
ISBN-13: 0817681922
DOWNLOAD EBOOK* First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.
Author: Anatoliĭ Moiseevich Vershik
Publisher: CRC Press
Published: 1990
Total Pages: 576
ISBN-13: 9782881246784
DOWNLOAD EBOOKEight papers provide mature readers with careful review of progress (through about 1983) toward the creation of a theory of the representations of infinite-dimensional Lie groups and algebras, and of some related topics. Recent developments in physics have provided major impetus for the development of such a theory, and the volume will be of special interest to mathematical physicists (quantum field theorists). Translated from the Russian edition of unstated date, and beautifully produced (which--at the price--it should be!). Book club price, $118. (NW) Annotation copyrighted by Book News, Inc., Portland, OR
Author: Seok-Jin Kang
Publisher: American Mathematical Soc.
Published: 1996
Total Pages: 242
ISBN-13: 0821805126
DOWNLOAD EBOOKOver the past 30 years, exciting developments in diverse areas of the theory of Lie algebras and their representations have been observed. The symposium covered topics such as Lie algebras and combinatorics, crystal bases for quantum groups, quantum groups and solvable lattice models, and modular and infinite-dimensional Lie algebras. In this volume, readers will find several excellent expository articles and research papers containing many significant new results in this area.
Author: Ian Malcolm Musson
Publisher: American Mathematical Soc.
Published: 2012-04-04
Total Pages: 512
ISBN-13: 0821868675
DOWNLOAD EBOOKLie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. This book develops the theory of Lie superalgebras, their enveloping algebras, and their representations. The book begins with five chapters on the basic properties of Lie superalgebras, including explicit constructions for all the classical simple Lie superalgebras. Borel subalgebras, which are more subtle in this setting, are studied and described. Contragredient Lie superalgebras are introduced, allowing a unified approach to several results, in particular to the existence of an invariant bilinear form on $\mathfrak{g}$. The enveloping algebra of a finite dimensional Lie superalgebra is studied as an extension of the enveloping algebra of the even part of the superalgebra. By developing general methods for studying such extensions, important information on the algebraic structure is obtained, particularly with regard to primitive ideals. Fundamental results, such as the Poincare-Birkhoff-Witt Theorem, are established. Representations of Lie superalgebras provide valuable tools for understanding the algebras themselves, as well as being of primary interest in applications to other fields. Two important classes of representations are the Verma modules and the finite dimensional representations. The fundamental results here include the Jantzen filtration, the Harish-Chandra homomorphism, the Sapovalov determinant, supersymmetric polynomials, and Schur-Weyl duality. Using these tools, the center can be explicitly described in the general linear and orthosymplectic cases. In an effort to make the presentation as self-contained as possible, some background material is included on Lie theory, ring theory, Hopf algebras, and combinatorics.
Author: Gerhard Paul Hochschild
Publisher:
Published: 1957
Total Pages: 62
ISBN-13:
DOWNLOAD EBOOKAuthor: Niky Kamran
Publisher: American Mathematical Soc.
Published: 1994
Total Pages: 322
ISBN-13: 0821851691
DOWNLOAD EBOOKThis volume, which contains a good balance of research and survey papers, presents at look at some of the current development in this extraordinarily rich and vibrant area.
Author: V. S. Varadarajan
Publisher: Prentice Hall
Published: 1974
Total Pages: 456
ISBN-13:
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