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arXiv · 2611.09360

The center of an associative crossed module

Emzar Khmaladze·Manuel Ladra·David Quiroga·Brais Ramos Pérez
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Abstract

In this paper, we define a Drinfeld-type center for an associative crossed module and prove that it is canonically the internal category of an explicit crossed module constructed from Mac Lane's bimultiplications. The resulting center carries a canonical multiplicative lifting, which induces a natural strict braiding, establishing its correspondence to a braided crossed module. We also examine the relationship between this center and Huq's categorical center. Finally, we obtain a canonical comparison morphism with Pirashvili's center of Lie crossed modules via the (braided) Liezation functors, which preserves braidings under an injectivity condition.

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Emzar Khmaladze, Manuel Ladra, David Quiroga, Brais Ramos Pérez. 2026-11-06. The center of an associative crossed module. https://arxiv.org/abs/2611.09360

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