Abstract We study actions of bosonizations of quantum linear spaces on quantum algebras. Under mild conditions, we classify actions on quantum affine spaces and quantum matrix algebras. In the former case, it is shown that all actions of generalized Taft algebras are trivial extensions of actions on quantum planes. In both cases we achieve bounds on the rank of the bosonization acting on the algebra.

中文翻译：

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量子线性空间对量子代数的作用

摘要 我们研究了量子线性空间玻色化对量子代数的作用。在温和的条件下，我们对量子仿射空间和量子矩阵代数的作用进行分类。在前一种情况下，表明广义塔夫脱代数的所有动作都是量子平面上动作的平凡扩展。在这两种情况下，我们都实现了作用于代数的玻色化等级的界限。