Skip to main content Accessibility help
×
  1. Home
  2. Books
  3. Representations of Lie Algebras
  • Cited by 1
      • Show more authors
      • You may already have access via personal or institutional login
    • Select format
    • Publisher:
      Cambridge University Press
      Publication date:
      05 November 2012
      16 August 2012
      ISBN:
      9781139236126
      9781107653610
      DOI:
      https://doi.org/10.1017/CBO9781139236126
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.25kg, 168 Pages
      • Subjects:
      Mathematics (general), Mathematics, Algebra
      Series:
      Australian Mathematical Society Lecture Series (22)
    You may already have access via personal or institutional login
    • Selected: Digital
    Add to cart View cart Buy from Cambridge.org
    Subjects:
    Mathematics (general), Mathematics, Algebra
    Series:
    Australian Mathematical Society Lecture Series (22)
    Information

    Book description

    This bold and refreshing approach to Lie algebras assumes only modest prerequisites (linear algebra up to the Jordan canonical form and a basic familiarity with groups and rings), yet it reaches a major result in representation theory: the highest-weight classification of irreducible modules of the general linear Lie algebra. The author's exposition is focused on this goal rather than aiming at the widest generality and emphasis is placed on explicit calculations with bases and matrices. The book begins with a motivating chapter explaining the context and relevance of Lie algebras and their representations and concludes with a guide to further reading. Numerous examples and exercises with full solutions are included. Based on the author's own introductory course on Lie algebras, this book has been thoroughly road-tested by advanced undergraduate and beginning graduate students and it is also suited to individual readers wanting an introduction to this important area of mathematics.

    Reviews

    'This short book develops the standard tools (special bases, duality, tensor decompositions, Killing forms, Casimir operators …) and aims for a single result: the classification of integral modules over gln. Requiring only basic linear algebra, this book can serve as an interesting alternative platform (to basic group theory) for introducing abstract algebra … Recommended.'

    D. V. Feldman Source: Choice

    Refine List

    Actions for selected content:

    Select all | Deselect all
    • View selected items
    • Export citations
    • Download PDF (zip)
    • Save to Kindle
    • Save to Dropbox
    • Save to Google Drive

    Save Search

    You can save your searches here and later view and run them again in "My saved searches".

    Please provide a title, maximum of 40 characters.
    Cancel
    ×

    Contents

    Contents
    References
    References
    References
    [1] N., Bourbaki, Lie Groups and Lie Algebras, 3 vols., Springer-Verlag, 1989 (Chapters 1–3), 2002 (Chapters 4–6), 2005 (Chapters 7–9).
    [2] R.W., Carter, Lie Algebras of Finite and Affine Type, vol. 96 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, 2005.
    [3] R. W., Carter, G., Segal, and I. G., Macdonald, Lectures on Lie Groups and Lie Algebras, vol. 32 of London Mathematical Society Student Texts, Cambridge University Press, 1995.
    [4] K. E, Rdmann and M. J., Wildon, Introduction to Lie Algebras, Springer Undergraduate Mathematics Series, Springer-Verlag, 2006.
    [5] W., Fulton, Young Tableaux, vol. 35 of London Mathematical Society Student Texts, Cambridge University Press, 1997.
    [6] W., Fulton and J., Harris, Representation Theory: A First Course, vol. 129 of Graduate Texts in Mathematics, Springer-Verlag, 1991.
    [7] R., Goodman and N. R., Wallach, Representations and Invariants of the Classical Groups, vol. 68 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, 1998.
    [8] B. C., Hall, Lie Groups, Lie Algebras, and Representations: An Elementary Introduction, vol. 222 of Graduate Texts in Mathematics, Springer-Verlag, 2003.
    [9] J., Hong and S.–J., Kang, Introduction to Quantum Groups and Crystal Bases, vol.42 of Graduate Studies in Mathematics, American Mathematical Society, 2002.
    [10] J. E., Humphreys, Introduction to Lie Algebras and Representation Theory, vol. 9 of Graduate Texts in Mathematics, Springer-Verlag, 1972.
    [11] J. C., Jantzen, Lectures on Quantum Groups, vol. 6 of Graduate Studies in Mathematics, American Mathematical Society, 1996.
    [12] V. G., Kac, Infinite-Dimensional Lie Algebras, 3rd edn, Cambridge University Press, 1990.
    [13] A. W., Knapp, Lie Groups: Beyond an Introduction, 2nd edn, vol. 140 of Progress in Mathematics, Birkhäuser, 2002.
    [14] I. G., Macdonald, Symmetric Functions and Hall Polynomials, 2nd edn, Oxford University Press, 1995.
    [15] W., Rossmann, Lie Groups: An Introduction Through Linear Groups, vol. 5 of Oxford Graduate Texts in Mathematics, Oxford University Press, 2002.

    Metrics

    Full text views

    Total number of HTML views: 0
    Total number of PDF views: 0 *
    Loading metrics...

    Book summary page views

    Total views: 0 *
    Loading metrics...

    * Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

    Usage data cannot currently be displayed.

    Accessibility standard: Unknown

    Why this information is here

    This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

    Accessibility Information

    Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.