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Mac Lane (co)homology

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Cyclic Homology

Part of the book series: Grundlehren der mathematischen Wissenschaften ((GL,volume 301))

Abstract

The second Hochschild cohomology group of rings (that is algebras over k = Z) classifies the extensions of a ring by a bimodule provided that the ex-tensions are split as abelian groups. In order to classify non-split extensions, Mac Lane introduced in the fifties the so-called Mac Lane (co)homology theory, that we denote by HML and which is closely related to the cohomology of the Eilenberg-Mac Lane spaces. Hochschild (co)homology and Mac Lane (co)homology coincide when the ring contains the rational numbers, but they differ in general.

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Authors
  1. Jean-Louis Loday
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  2. Teimuraz Pirashvili
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© 1998 Springer-Verlag Berlin Heidelberg

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Loday, JL., Pirashvili, T. (1998). Mac Lane (co)homology. In: Cyclic Homology. Grundlehren der mathematischen Wissenschaften, vol 301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11389-9_13

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  • DOI: https://doi.org/10.1007/978-3-662-11389-9_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08316-7

  • Online ISBN: 978-3-662-11389-9

  • eBook Packages: Springer Book Archive

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