Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations
Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations
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DOI：
10.1007/b83849
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发表时间：
2002-09
期刊：
影响因子：
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通讯作者：
S. Caenepeel;G. Militaru;Shenglin Zhu
中科院分区：
文献类型：
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作者：
S. Caenepeel;G. Militaru;Shenglin Zhu
Doi-Koppinen Hopf模和Ensemble模统一了过去几十年来被广泛研究的各种模，如Hopf模，分次模，Yetter-Drinfeld模。这本书提出了一个统一的理论，重点是范畴概念概括的概念，可分和弗罗贝纽斯代数，并讨论与粉碎产品，伽罗瓦理论和下降理论的关系。第二部分的每一章都专门讨论一个特定的非线性方程。这篇文章的组织方式使得这四个方程之间的类比很清楚：量子杨-巴克斯特方程与Yetter-Drinfeld模有关，五边形方程与Hopf模有关，朗方程与朗双模有关。Frobenius-可分性方程为研究Frobenius和可分代数提供了一个新的视角。
Doi-Koppinen Hopf modules and entwined modules unify various kinds of modules that have been intensively studied over the past decades, such as Hopf modules, graded modules, Yetter-Drinfeld modules. The book presents a unified theory, with focus on categorical concepts generalizing the notions of separable and Frobenius algebras, and discussing relations with smash products, Galois theory and descent theory. Each chapter of Part II is devoted to a particular nonlinear equation. The exposé is organized in such a way that the analogies between the four are clear: the quantum Yang-Baxter equation is related to Yetter-Drinfeld modules, the pentagon equation to Hopf modules, and the Long equation to Long dimodules. The Frobenius-separability equation provides a new viewpoint to Frobenius and separable algebras.