Synopsis for C2.2b: Homological Algebra
Number of lectures: 16 HT
Course Description
Level: M-level \hfill Method of Assessment: Written examination.
Weight: Half-unit (OSS paper code tbc).
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)
Weight: Half-unit (OSS paper code tbc).
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
books.google.co.uk/books/about/An_introduction_to_homological_algebra.html?id=flm-dBXfZ_gC&redir_esc=y
Last updated by Yakov Kremnitzer on Mon, 04/03/2013 - 12:14am.
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This page is maintained by Nia Roderick. Please use the contact form for feedback and comments.