Two-cocycles and cleft extensions in left braided categories

Heckenberger Istvan; Wolf Kevin

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Two-cocycles and cleft extensions in left braided categories

机译：左编织类别的两栖卷和裂隙延伸

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摘要

We define two-cocycles and cleft extensions in categories that are not necessarily braided, but where specific objects braid from one direction, like for a Hopf algebra H a Yetter-Drinfeld module braids from the left with H-modules. We will generalize classical results to this context and give some application for the categories of Yetter-Drinfeld modules and H-modules. In particular, we will describe liftings of coradically graded Hopf algebras in the category of Yetter-Drinfeld modules with these techniques.

机译：我们在不一定是编织的类别中定义了两个余环和分裂扩张，但其中特定对象从一个方向编织，比如Hopf代数H a Yetter-Drinfeld模从左侧编织H-模。我们将把经典结果推广到这种情况，并给出Yetter-Drinfeld模和H-模范畴的一些应用。特别地，我们将用这些技巧描述Yetter-Drinfeld模范畴中的珊瑚分次Hopf代数的提升。

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来源
《Journal of algebra and its applications》 |2021年第1期|共21页
作者
Heckenberger Istvan; Wolf Kevin;
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作者单位

Philipps Univ Marburg FB Math &

Inforrnat Hans Meerwein Str D-35032 Marburg Germany;

Philipps Univ Marburg FB Math &

Inforrnat Hans Meerwein Str D-35032 Marburg Germany;

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原文格式 PDF
正文语种 eng
中图分类代数、数论、组合理论;
关键词
Braided monoidal category; braided Hopf algebra; Yetter-Drinfeld module; lifting;

机译：编织长尾图;编织Hopf代数;Derter-Drinfeld模块;提升;

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Two-cocycles and cleft extensions in left braided categories

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