This paper gives a Maschke-type theorem over semisimple weak Hopf algebras,extends the well-known Maschke-type theorem given by Cohen and Fishman and constructs a Morita context over weak Hopf algebras.
In this paper we mainly give Maschke-type theorems for weak smash coproduct coalgebras which simultaneously show how to deal with the complicated computations of weak smash coproduct coalgebras.
Let(H,αH,βH,ψH,ωH,SH)be a BiHom-Hopf algebra and(A,αA,βA)be an(H,αH,βH,ψH,ωH)-BiHom-bimodule algebra,where the mapsαH,βH,ψH,ωH,αA,βA are bijective.We first prove the Maschke-type theorem for the BiHom-...Let(H,αH,βH,ψH,ωH,SH)be a BiHom-Hopf algebra and(A,αA,βA)be an(H,αH,βH,ψH,ωH)-BiHom-bimodule algebra,where the mapsαH,βH,ψH,ωH,αA,βA are bijective.We first prove the Maschke-type theorem for the BiHom-L-R smash product over a finite-dimensional semisimple BiHom-Hopf algebra.Next we give a Morita context between the BiHom-subalgebra A^(biH)and the BiHom-L-R smash product A#H.展开更多
We obtain necessary and sufficient conditions for the functor F ： ∪/Ac （ψ） → Mc on the category of partial entwined modules that forgets the A-action to be separable. As an application, we prove a Maschke-type t...We obtain necessary and sufficient conditions for the functor F ： ∪/Ac （ψ） → Mc on the category of partial entwined modules that forgets the A-action to be separable. As an application, we prove a Maschke-type theorem for the category of partial entwined modules.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.10571153)the Postdoctoral Science Foundation of China(Grant No.2005037713)the Postdoctoral Science Foundation of Jiangsu(Grant No.0203003403).
文摘This paper gives a Maschke-type theorem over semisimple weak Hopf algebras,extends the well-known Maschke-type theorem given by Cohen and Fishman and constructs a Morita context over weak Hopf algebras.
基金the National Natural Science Foundation of China (No.10571153)the Educational Ministry Science Technique Research Key Foundation of China (No.108154)the Grant for Young Teachers of Nanjing Agricultural University (No.KJ06025)
文摘This paper mainly gives a Maschke-type theorem for two-sided weak smash products over semisimple weak Hopf algebras.
基金the Program for New Century Excellent Talents in University (No.04-0522)The Funds for Doctor of Ludong University (No.LY20062703)
文摘In this paper we mainly give Maschke-type theorems for weak smash coproduct coalgebras which simultaneously show how to deal with the complicated computations of weak smash coproduct coalgebras.
基金supported by the NSF of China(Nos.11801515,12071441)the Natural Science Foundation of Zhejiang Province(No.LY20A010003)the Foundation of Zhejiang Educational Committee(No.Y201942625).
文摘Let(H,αH,βH,ψH,ωH,SH)be a BiHom-Hopf algebra and(A,αA,βA)be an(H,αH,βH,ψH,ωH)-BiHom-bimodule algebra,where the mapsαH,βH,ψH,ωH,αA,βA are bijective.We first prove the Maschke-type theorem for the BiHom-L-R smash product over a finite-dimensional semisimple BiHom-Hopf algebra.Next we give a Morita context between the BiHom-subalgebra A^(biH)and the BiHom-L-R smash product A#H.
基金The work is supported by the Key University Science Research Project of Anhui Province （KJ2015A294）, the China Postdoctoral Science Foundation （2015M571725）, the Fund of Science and Technology Department of Guizhou Province （2014GZ81365） and the Program for Science and Technology Innovation Talents in Education Department of Guizhou Province （KY[20151481）.
文摘We obtain necessary and sufficient conditions for the functor F ： ∪/Ac （ψ） → Mc on the category of partial entwined modules that forgets the A-action to be separable. As an application, we prove a Maschke-type theorem for the category of partial entwined modules.
