Synopsis for Homological Algebra
Number of lectures: 16 HT
Course Description
Synopsis
Chain complexes: complexes of R-modules, operations on chain complexes, long exact sequences, chain homotopies, mapping cones and cylinders (3 hours) Derived functors: delta functors, projective and injective resolutions, left and right derived functors (4 hours) Tor and Ext: Tor and flatness, Ext and extensions, universal coefficients theorems (3 hours) Group homology and cohomology: definition, interpretation of
and 
, universal central extensions, the Bar resolution (3 hours)
Lie algebra homology and cohomology: Lie algebras and universal enveloping algebras, definition of homology and cohomology and relations to Tor and Ext, and , universal central extensions (3 hours)Reading List
Weibel, Charles An introduction to Homological algebra
http://books.google.co.uk/books/about/An\_introduction\_to\_homological\_algebra.html?id=flm-dBXfZ\_gC&redir\_esc=y
Last updated by Nia Roderick on Fri, 12/10/2012 - 12:49pm.
This page is maintained by Nia Roderick. Please use the contact form for feedback and comments.
This page is maintained by Nia Roderick. Please use the contact form for feedback and comments.