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  3. Lie Algebras of Finite and Affine Type
  • Cited by 114
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    • Publisher:
      Cambridge University Press
      Publication date:
      January 2010
      October 2005
      ISBN:
      9780511614910
      9780521851381
      DOI:
      https://doi.org/10.1017/CBO9780511614910
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      1.04kg, 652 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Algebra
      Series:
      Cambridge Studies in Advanced Mathematics (96)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Algebra
    Series:
    Cambridge Studies in Advanced Mathematics (96)
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    Book description

    Lie algebras have many varied applications, both in mathematics and mathematical physics. This book provides a thorough but relaxed mathematical treatment of the subject, including both the Cartan-Killing-Weyl theory of finite dimensional simple algebras and the more modern theory of Kac-Moody algebras. Proofs are given in detail and the only prerequisite is a sound knowledge of linear algebra. The first half of the book deals with classification of the finite dimensional simple Lie algebras and of their finite dimensional irreducible representations. The second half introduces the theory of Kac-Moody algebras, concentrating particularly on those of affine type. A brief account of Borcherds algebras is also included. An Appendix gives a summary of the basic properties of each Lie algebra of finite and affine type.

    Reviews

    "This monograph provides a crystal clear exposition of the theory of finite-dimensional simple Lie algebras and a nice introduction to (infinite-dimensional) Kac - Moody algebras of affine type. Also, an excellent course on Lie algebras could be constructed starting from the book."
    Daniel Beltita, Institute of Mathematics, Romanian Academy, SIAM Review

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