An Introduction to Homological Algebra [Paperback]

A portrait of the subject of homological algebra as it exists today.The landscape of homological algebra has evolved over the past half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today, including historical connections with topology, regular local rings, and semi-simple Lie algebras.The landscape of homological algebra has evolved over the past half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today, including historical connections with topology, regular local rings, and semi-simple Lie algebras.The landscape of homological algebra has evolved over the past 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 is also described. 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.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. It is...the ideal text for the working mathematician need- ing a detailed del$