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Developments and Retrospectives in Lie Theory

Algebraic Methods

  • Book
  • © 2014

Overview

Editors:
  1. Geoffrey Mason

    1. Department of Mathematics, University of California, Santa Cruz, Santa Cruz, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Ivan Penkov

    1. Jacobs University, Bremen, Germany

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    You can also search for this editor in PubMed   Google Scholar

  3. Joseph A. Wolf

    1. Department of Mathematics, University of California, Berkeley, Berkeley, USA

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    You can also search for this editor in PubMed   Google Scholar

  • Includes contributions from an international group of experts in representation and Lie theory
  • Reflects the widespread influence of the Lie Theory Workshop on areas such as harmonic analysis, differential and algebraic geometry, and number theory
  • Contains articles covering representation theory from algebraic, geometric, analytic, and topological perspectives

Part of the book series: Developments in Mathematics (DEVM, volume 38)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Group Gradings on Lie Algebras, with Applications to Geometry. I

    • Yuri Bahturin, Michel Goze, Elisabeth Remm
    Pages 1-50

  3. Bounding the Dimensions of Rational Cohomology Groups

    • Christopher P. Bendel, Brian D. Boe, Christopher M. Drupieski, Daniel K. Nakano, Brian J. Parshall, Cornelius Pillen et al.
    Pages 51-69

  4. Representations of the General Linear Lie Superalgebra in the BGG Category \(\mathcal{O}\)

    • Jonathan Brundan
    Pages 71-98

  5. Three Results on Representations of Mackey Lie Algebras

    • Alexandru Chirvasitu
    Pages 99-109

  6. Free Field Realizations of the Date-Jimbo-Kashiwara-Miwa Algebra

    • Ben Cox, Vyacheslav Futorny, Renato Alessandro Martins
    Pages 111-136

  7. The Deformation Complex is a Homotopy Invariant of a Homotopy Algebra

    • Vasily Dolgushev, Thomas Willwacher
    Pages 137-158

  8. Invariants of Artinian Gorenstein Algebras and Isolated Hypersurface Singularities

    • Michael Eastwood, Alexander Isaev
    Pages 159-173

  9. Generalized Loop Modules for Affine Kac–Moody Algebras

    • Vyacheslav Futorny, Iryna Kashuba
    Pages 175-183

  10. Twisted Localization of Weight Modules

    • Dimitar Grantcharov
    Pages 185-206

  11. Dirac Cohomology and Generalization of Classical Branching Rules

    • Jing-Song Huang
    Pages 207-228

  12. Cleft Extensions and Quotients of Twisted Quantum Doubles

    • Geoffrey Mason, Siu-Hung Ng
    Pages 229-246

  13. On the Structure of \(\mathbb{N}\)-Graded Vertex Operator Algebras

    • Geoffrey Mason, Gaywalee Yamskulna
    Pages 247-274

  14. Variations on a Casselman–Osborne Theme

    • Dragan Miličić
    Pages 275-289

  15. Tensor Representations of Mackey Lie Algebras and Their Dense Subalgebras

    • Ivan Penkov, Vera Serganova
    Pages 291-330

  16. Algebraic Methods in the Theory of Generalized Harish-Chandra Modules

    • Ivan Penkov, Gregg Zuckerman
    Pages 331-350

  17. On Exceptional Vertex Operator (Super) Algebras

    • Michael P. Tuite, Hoang Dinh Van
    Pages 351-384

  18. The Cubic, the Quartic, and the Exceptional Group G2

    • Anthony van Groningen, Jeb F. Willenbring
    Pages 385-397
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Keywords

About this book

The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades. These workshops have been sponsored by the NSF, noting the talks have been seminal in describing new perspectives in the field covering broad areas of current research. At the beginning, the top universities in California and Utah hosted the meetings which continue to run on a quarterly basis. Experts in representation theory/Lie theory from various parts of the US, Europe, Asia (China, Japan, Singapore, Russia), Canada, and South and Central America were routinely invited to give talks at these meetings. Nowadays, the workshops are also hosted at universities in Louisiana, Virginia, and Oklahoma. The contributors to this volume have all participated in these Lie theory workshops and include in this volume expository articles which cover representation theory from the algebraic, geometric, analytic, and topological perspectives with also important connections to math physics. These survey articles, review and update the prominent seminal series of workshops in representation/Lie theory mentioned-above, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, number theory, and mathematical physics. Many of the contributors have had prominent roles in both the classical and modern developments of Lie theory and its applications.

Editors and Affiliations

  • Department of Mathematics, University of California, Santa Cruz, Santa Cruz, USA

    Geoffrey Mason

  • Jacobs University, Bremen, Germany

    Ivan Penkov

  • Department of Mathematics, University of California, Berkeley, Berkeley, USA

    Joseph A. Wolf

Bibliographic Information

  • Book Title: Developments and Retrospectives in Lie Theory

  • Book Subtitle: Algebraic Methods

  • Editors: Geoffrey Mason, Ivan Penkov, Joseph A. Wolf

  • Series Title: Developments in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-09804-3

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2014

  • Hardcover ISBN: 978-3-319-09803-6Published: 26 November 2014

  • Softcover ISBN: 978-3-319-37820-6Published: 10 September 2016

  • eBook ISBN: 978-3-319-09804-3Published: 31 October 2014

  • Series ISSN: 1389-2177

  • Series E-ISSN: 2197-795X

  • Edition Number: 1

  • Number of Pages: X, 397

  • Number of Illustrations: 85 b/w illustrations

  • Topics: Topological Groups, Lie Groups, Algebraic Geometry, Number Theory

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