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On representation of quasi-Hopf group coalgebras

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Published/Copyright: April 30, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 1

Abstract

In this paper, we give the definitions of crossed quasi-Hopf π-coalgebra H and a crossed left π-H-modules, and show that the category of crossed left π-H-modules is a monoidal category. Finally, we show that a family R = {Rα, β∈ Hα⊗ Hβ} of elements is a quasitriangular structure of a crossed quasi-Hopf π-coalgebra H if and only if the category of crossed left π-H-modules over H is a braided monoidal category with braiding defined by R.

Keywords: quasi-Hopf π-coalgebra; braided monoidal category; quasitriangular structure
MSC: Primary 16T05

The work is supported by the TianYuan Special Funds of the National Natural Science Foundation of China (No. 11426073), the NSF of Jiangsu Province (No. BK2012736) and the Fund of Science and Technology Department of Guizhou Province (No. 2014GZ81365) and the Program for Science and Technology Innovation Talents in Education Department of Guizhou Province (No. KY[2015]481).

  1. This paper has been communicated by Sylvia Pulmannová

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Received: 2012-12-19
Accepted: 2013-4-24
Published Online: 2016-4-30
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0115
Keywords for this article
quasi-Hopf π-coalgebra; braided monoidal category; quasitriangular structure

Articles in the same Issue

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  2. Prof. RNDr. Ján Jakubík, DrSc. passed away
  3. Research Article
  4. On the number of slim, semimodular lattices
  5. Research Article
  6. Quantum computational algebra with a non-commutative generalization
  7. Research Article
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  9. Research Article
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  12. On representation of quasi-Hopf group coalgebras
  13. Research Article
  14. On the q-Bernstein polynomials of the logarithmic function in the case q > 1
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  17. Research Article
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