Introduction to Homological Algebra (English Edition) (English Edition)

Author: Weber
Publisher:
Publish Date: 2004-11-01
Features: Homological algebra has evolved into a fundamental tool for mathematicians in the latter half of the 20th century. This book discusses the basic concepts of modern homological algebra and elaborates on the historical origins of its connections with topology, regular local rings, and semisimple Lie algebras. The first half of the book covers canonical topics in homological algebra, such as derived functors, Tor and Ext functors, perspective dimension, and spectral sequences, with explanations through group homology and Lie algebra. It also includes some less canonical topics, such as the derived inverse limit functor lim, local cohomology, Galois cohomology, and affine Lie algebras. The second half of the book discusses some non-traditional topics, which are important parts of the modern homological mathematical toolbox, such as simplicial methods, Hochschild and cyclic homology, derived categories, and total derived functors. By demonstrating the use of these tools, the book helps beginners overcome the technical barriers of homological algebra.