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    An Introduction to Homological Algebra (Cambridge Studies in Advanced Mathematics (Paperback)) (Paperback) By (author) Charles A. Weibel, Series edited by B. Bollobas, Series edited by W. Fulton, Series edited by A. Katok, Series edited by F. Kirwan, Series edited by P. Sarnak, Series edited by B. Simon, Series edited by B. Totaro

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    DescriptionThe landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described. This book is suitable for second or third year graduate students. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. By making these tools more accessible, the book helps to break down the technological barrier between experts and casual users of homological algebra.


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  • Full bibliographic data for An Introduction to Homological Algebra

    Title
    An Introduction to Homological Algebra
    Authors and contributors
    By (author) Charles A. Weibel, Series edited by B. Bollobas, Series edited by W. Fulton, Series edited by A. Katok, Series edited by F. Kirwan, Series edited by P. Sarnak, Series edited by B. Simon, Series edited by B. Totaro
    Physical properties
    Format: Paperback
    Number of pages: 468
    Width: 152 mm
    Height: 228 mm
    Thickness: 32 mm
    Weight: 680 g
    Language
    English
    ISBN
    ISBN 13: 9780521559874
    ISBN 10: 0521559871
    Classifications

    BIC E4L: MAT
    B&T Book Type: NF
    Nielsen BookScan Product Class 3: S7.9T
    Ingram Subject Code: SE
    Libri: I-SE
    B&T General Subject: 710
    BIC subject category V2: PBF
    Abridged Dewey: 512
    BISAC V2.8: SCI000000
    Warengruppen-Systematik des deutschen Buchhandels: 26240
    BISAC V2.8: MAT002000
    B&T Merchandise Category: UP
    DC20: 512.55
    DC22: 512.8
    Thema V1.0: PBF
    Edition
    2
    Edition statement
    Revised.
    Illustrations note
    black & white illustrations
    Publisher
    CAMBRIDGE UNIVERSITY PRESS
    Imprint name
    CAMBRIDGE UNIVERSITY PRESS
    Publication date
    13 January 2002
    Publication City/Country
    Cambridge
    Review quote
    "It is...the ideal text for the working mathematician need- ing a detailed description of the fundamentals of the subject as it exists and is used today; the author has succeeded brilliantly in his avowed intention to break down 'the technological barriers between casual users and experts'." Kenneth A. Brown, Mathematical Reviews "By collecting, organizing, and presenting both the old and the new in homological algebra, Weibel has performed a valuable service. He has written a book that I am happy to have in my library." Joseph Rotman, Bulletin of the American Mathematical Society
    Table of contents
    1. Chain complexes; 2. Derived functors; 3. Tor and Ext; 4. Homological dimensions; 5. Spectral sequences; 6. Group homology and cohomology; 7. Lie algebra homology and cohomology; 8. Simplicial methods in homological algebra; 9. Hothschild and cyclic homology; 10. The derived category; Appendix: category theory language.