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Finally, we obtain the duality theorem of π-crossed product A#πσH, generalizing Corollary 5.8 in the authors’ paper.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:Let π be a group and let H = {Hα}α∈π be a Hopf π-coalgebra in the sense of Turaev .
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Temel Bulgular & Veri:Let H act weakly on an algebra A and σ : H1⊗H1 → Aa k-linear map.
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Sonuç & Katkı:Finally, we obtain the duality theorem of π-crossed product A#πσH, generalizing Corollary 5.8 in the authors’ paper.
🔬Tür:Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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.
Anahtar kelimeler
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Bu Makaleye Atıf Yap
Shen, B., Wang, S. (2008). ON GROUP CROSSED PRODUCTS. International Electronic Journal of Algebra, Volume: 4 Issue: 4. https://ajindex.com/articles/1588350