✨
AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Finally, we obtain the duality theorem of π-crossed product A#πσH, generalizing Corollary 5.8 in the authors’ paper.
📌 3 Key Takeaways
🎯
Objective & Hypothesis:Let π be a group and let H = {Hα}α∈π be a Hopf π-coalgebra in the sense of Turaev .
📊
Key Findings & Data:Let H act weakly on an algebra A and σ : H1⊗H1 → Aa k-linear map.
💡
Conclusion & Impact:Finally, we obtain the duality theorem of π-crossed product A#πσH, generalizing Corollary 5.8 in the authors’ paper.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Hopf group-coalgebra · group-crossed product · duality theorem
Abstract
Let π be a group and let H = {Hα}α∈π be a Hopf π-coalgebra in the sense of Turaev . Let H act weakly on an algebra A and σ : H1⊗H1 → Aa k-linear map. Then we first introduce the notion of a π-crossed product A#πσH = {A#σHα}α∈π and find some sufficient and necessary conditions under which each A#σHα forms an algebra. Next we define a comultiplication, a counit and an antipode on A#πσH making it into a Hopf π-coalgebra. Finally, we obtain the duality theorem of π-crossed product A#πσH, generalizing Corollary 5.8 in the authors’ paper.
🔖
Cite This Article
SHEN, B., WANG, S. (2008). ON GROUP CROSSED PRODUCTS. International Electronic Journal of Algebra, Cilt: 4 - Sayı: 4, 177–188. https://ajindex.com/articles/832570