弱霍普夫布拉斯、粉碎乘积及其在邻接稳定布拉斯中的应用

Pub Date : 2024-01-24 DOI:10.1142/s0219498825501567
Zhimin Liu, Shenglin Zhu
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引用次数: 0

摘要

对于特征为零的域 k 上的半简单准三角形霍普夫代数(H,R)和强可分离量子交换 H 模块代数 A,我们证明 A#H 是弱霍普夫代数,并且它可以嵌入弱霍普夫代数 EndA∗⊗H 中。有了这些结构,A#HMod 就是科恩和韦斯特里希引入的单元范畴,而 EndA∗⊗Hℳ 与 Hℳ 是张量等价的。如果 A 位于 Hℳ 的 Müger 中心,那么嵌入就是准三角形弱霍普夫代数态射。这就解释了在有限群代数的不可还原Yetter-Drinfeld模块的表征中存在子群包含的原因。
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Weak Hopf algebras, smash products and applications to adjoint-stable algebras

For a semisimple quasi-triangular Hopf algebra (H,R) over a field k of characteristic zero, and a strongly separable quantum commutative H-module algebra A, we show that A#H is a weak Hopf algebra, and it can be embedded into a weak Hopf algebra EndAH. With these structures, A#HMod is the monoidal category introduced by Cohen and Westreich, and EndAH is tensor equivalent to H. If A is in the Müger center of H, then the embedding is a quasi-triangular weak Hopf algebra morphism. This explains the presence of a subgroup inclusion in the characterization of irreducible Yetter–Drinfeld modules for a finite group algebra.

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