Previous Talks

March 17

Speaker: Guilherme Cruz (IME-USP)

Title: Hochschild (co)-homology: definitions and examples (Slides) (Exercises)

Abstract: In this seminar, our main goal consists on introducing the definition of Hochschild (co)-homology. For that we follow two approaches, the first one relies on an explicit complex, while the second one is given by mean of the functors Ext and Tor. Also, we will see which properties of an associative algebra are detected by its Hochschild (co)-homology. Each of the mathematical concepts contained in this abstract will be introduced along the talk.

References: 

• 1. C. Kassel, 'Homology and cohomology of associative algebras. A concise introduction to cyclic homology”. Advanced School on Non-commutative Geometry ICTP, Trieste, August 2004. 

  2. C. Weibel, An Introduction to Homological Algebra", Vol. 38. Cambridge Studies in Advanced Mathematics. 1994.

  3. Jean-Louis Loday, Cyclic Homology", Vol. 301. Grundlehren der mathematischen Wissenschaften. 2nd edition. Springer Verlag, 1998.

  4. G. Hochschild, “On the Cohomology Groups of an Associative Algebra”. Annals of Mathematics 46 (1) (1945), pp. 58–67.

  5. H. Cartan, S. Eilenberg, Homological Algebra", Princeton University Press, 1956.