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Third Mac Lane cohomology

Published online by Cambridge University Press:  01 March 2008

HANS–JOACHIM BAUES ,
MAMUKA JIBLADZE  and
TEIMURAZ PIRASHVILI
HANS–JOACHIM BAUES
Affiliation:
Max-Planck-Institut für Mathematik, Vivatsgasse 7, Bonn 53111, Germany. e-mail: baues@mpim-bonn.mpg.de
MAMUKA JIBLADZE
Affiliation:
Razmadze Mathematical Institute, Alexidze st. 1, Tbilisi 0193, Georgia. e-mail: jib@rmi.acnet.ge
TEIMURAZ PIRASHVILI
Affiliation:
Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH. e-mail: tp59-at-le.ac.uk
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Abstract

MacLane cohomology is an algebraic version of the topological Hochschild cohomology. Based on the computation of the third author (see Appendix) we obtain an interpretation of the third Mac Lane cohomology of rings using certain kind of crossed extensions of rings in the quadratic world. Actually we obtain two such interpretations corresponding to the two monoidal structures on the category of square groups.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 144 , Issue 2 , March 2008 , pp. 337 - 367
Copyright
Copyright © Cambridge Philosophical Society 2008

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