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/tropical-homological-algebra

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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

  K-regularity, cdh-fibrant 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 Costello-Gwilliam 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/how-exactly-is-hochschild-homology-a-monad-homology

  http://mathoverflow.net/questions/39726/hochschild-homology-of-dgas

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• Comments Posted

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• General Introduction
• Search results
• Online References
• Paper References
• Definition
• Properties
• Standard theorems
• Open Problems
• Connections to Number Theory
• Computations and Examples
• History and Applications
• Some Research Articles
• Other Information
• Comments Posted
• Comments