Introduction to Homological Algebra

ISBN-10: 0521559871
ISBN-13: 9780521559874
Edition: N/A
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Description: The 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  More...

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Book details

Publisher: Cambridge University Press
Publication date: 10/27/1995
Binding: Paperback
Pages: 468
Size: 6.25" wide x 9.25" long x 1.25" tall
Weight: 2.002
Language: English

The 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.

Chain complexes
Derived functors
Tor and Ext
Homological dimensions
Spectral sequences
Group homology and cohomology
Lie algebra homology and cohomology
Simplicial methods in homological algebra
Hothschild and cyclic homology
The derived category
Appendix: category theory language

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