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An explicit description of the second cohomology group of a quandle

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Abstract

We use the inflation-restriction sequence and a result of Etingof and Graña on the rack cohomology to give a explicit description of 2-cocycles of finite indecomposable quandles with values in an abelian group. Several applications are given.

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Acknowledgements

We thank G. García and M. Kotchetov for interesting discussions. We also thank N. Andruskiewitsch for his constant guidance and support. This work was initiated while the authors were visiting María Ofelia Ronco, at Universidad de Talca, Chile. We are grateful for her warm hospitality. The authors are grateful to the reviewer for useful remarks, interesting suggestions and corrections.

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Authors and Affiliations

  1. FaMAF–CIEM (CONICET), Universidad Nacional de Córdoba, Medina Allende s/n, Ciudad Universitaria (5000), Córdoba, Argentina

    Agustín García Iglesias

  2. Departamento de Matemática – FCEN, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria (1428), Buenos Aires, Argentina

    Leandro Vendramin

Authors
  1. Agustín García Iglesias
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  2. Leandro Vendramin
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Corresponding author

Correspondence to Agustín García Iglesias.

Additional information

This work is partially supported by CONICET, FONCyT PICT-2013-1414 and PICT-2014-1376, Secyt (UNC), ICTP and MATH-AmSud.

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García Iglesias, A., Vendramin, L. An explicit description of the second cohomology group of a quandle. Math. Z. 286, 1041–1063 (2017). https://doi.org/10.1007/s00209-016-1794-7

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  • DOI: https://doi.org/10.1007/s00209-016-1794-7

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