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Classical Lie Algebras at Infinity

Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and rece...

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Bibliographic Details
Main Authors: Penkov, Ivan, Hoyt, Crystal (Author)
Format: eBook
Language:English
Published: Cham Springer International Publishing 2022, 2022
Edition:1st ed. 2022
Series:Springer Monographs in Mathematics
Subjects:
Lie Groups
Topological Groups And Lie Groups
Topological Groups
Algebra
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • Preface
  • Notation and Terminology. - I. Structure of Locally Reductive Lie Algebras
  • 1. Finite-dimensional Lie algebras
  • 2. Finite-dimensional Lie superalgebras
  • 3. Root-reductive Lie algebras
  • 4. Two generalizations
  • 5. Splitting Borel subalgebras of sl(infinity), frak o (infinity), sp(infinity) and generalized flags
  • 6. General Cartan, Borel and parabolic subalgebras of gl(infinity) and sl(infinity)
  • II. Modules over Locally Reductive Lie Algebras
  • 7. Tensor modules of sl(infinity), frak o(infinity), sp (infinity)
  • 8. Weight modules
  • 9.Generalized Harish-Chandra modules
  • III. Geometric aspects. - 10.The Bott-Borel-Weil Theorem
  • References
  • Index of Notation
  • Index

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