Hochschild homology

General Introduction
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Search results
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Online References
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Paper References
Chapter 9 in Weibel: An introduction to homological algebra.
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Definition
For a def in a very general context, see http://mathoverflow.net/questions/55018/tropicalhomologicalalgebra
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
Karoubi and Lambre on the Dennis trace map and algebraic number theory.
Nistor on the Hochschild homology of Hecke algebras
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Computations and Examples
Cortinas and Weibel: Homology of Azumaya algebras. Describes the Hochschild homology of Azumaya algs. It seems like there is a "reduced trace map isomorphism" between the HH of a matrix algebra over a ring and HH of the ring.
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History and Applications
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Some Research Articles
Kazhdan et al: K0222
Kregularity, cdhfibrant Hochschild homology, and a conjecture of Vorst , by G. Cortinas , C. Haesemeyer , and C. A. Weibel: K0783
E_n homology as functor homology http://front.math.ucdavis.edu/0907.1283
Talk by Greg Ginot  Derived Higher Hochschild theory. Abstract: Recently, various homology (or rather objects of some derived category) inspired by topological field theories have emerged, for instance CostelloGwilliam factorization algebras. Another one of this is given by higher Hochschild homology; this is a (derived) bifunctor associated to topological spaces and commutative differential graded algebras (=CDGA) with value in CDGA, which coincides with the usual Hochshcild complex when applied to a circle. We gave an axiomatic characterization of this bifunctor (as well as some nice corollaries of it) and explain its close relationship with locally constant factorization algebras. The key idea is to use a locality axiom which also implies a close relationship with Lurie's Topological chiral homology.
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Other Information
http://mathoverflow.net/questions/3078/howexactlyishochschildhomologyamonadhomology
http://mathoverflow.net/questions/39726/hochschildhomologyofdgas
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