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<p>The aim of this paper is twofold. Firstly, it gives an overview of the concept of the centre of a crossed module which was recently introduced by the author both in group theory and the Lie algebra framework. This centre is closely related to the Gottlieb group of the classifying space of a crossed module and also to the Drinfeld centre of a monoidal category introduced independently by Drinfeld and Joyal and Street. Secondly, this paper introduces the homotopy invariance property for the centre of a crossed module, which is a new result.</p>

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ON THE CENTRE OF CROSSED MODULES OF GROUPS

  • 期刊论文

  • 发表日期：

    2025年6月20日

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  • Mariam Pirashvili

摘要

The aim of this paper is twofold. Firstly, it gives an overview of the concept of the centre of a crossed module which was recently introduced by the author both in group theory and the Lie algebra framework. This centre is closely related to the Gottlieb group of the classifying space of a crossed module and also to the Drinfeld centre of a monoidal category introduced independently by Drinfeld and Joyal and Street. Secondly, this paper introduces the homotopy invariance property for the centre of a crossed module, which is a new result.