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On the conjectural Leibniz cohomology for groups

Published online by Cambridge University Press:  30 November 2012

Simon Covez
Simon Covez*
Affiliation:
University of Luxembourg, Campus Kirchberg Mathematics Research Unit, BLG, 6, rue Richard Coudenhove-Kalergi, L-1359 Luxembourg, Grand Duchy of Luxembourgsimon.covez@uni.lu
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Abstract

This article presents results which are consistent with conjectures about Leibniz (co)homology for discrete groups, due to J. L. Loday in 2003. We prove that rack cohomology has properties very close to the properties expected for the conjectural Leibniz cohomology. In particular, we prove the existence of a graded dendriform algebra structure on rack cohomology, and we construct a graded associative algebra morphism H•(−) → HR•(−) from group cohomology to rack cohomology which is injective for ● = 1.

Keywords

Leibniz algebradendriform algebraZinbiel algebrarack cohomologygroup cohomologyconjectural Leibniz K-theory

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Type
Research Article
Information
Journal of K-Theory , Volume 10 , Issue 3 , December 2012 , pp. 519 - 563
Copyright
Copyright © ISOPP 2012

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References

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