We study glued tensor and free products of compact matrix quantum groups with cyclic groups – so-called tensor and free complexifications. We characterize them by studying their representation categories and algebraic relations. In addition, we generalize the concepts of global colourization and alternating colourings from easy quantum groups to arbitrary compact matrix quantum groups. Those concepts are closely related to tensor and free complexification procedures. Finally, we also study a more general procedure of gluing and ungluing.

中文翻译：

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粘合紧凑矩阵量子组

我们研究具有循环基团的紧凑矩阵量子组的胶合张量和自由积-所谓的张量和自由络合。我们通过研究它们的表示类别和代数关系来表征它们。另外，我们概括了从简单的量子组到任意的紧凑矩阵量子组的全局着色和交替着色的概念。这些概念与张量和自由复杂化过程密切相关。最后，我们还研究了更通用的粘合和脱胶步骤。