The theory of L-R smash product is extended to multiplier Hopf algebras and a sufficient condition for L-R smash product to be regular multiplier Hopf algebras is given. In particular, the result of the paper implies ...The theory of L-R smash product is extended to multiplier Hopf algebras and a sufficient condition for L-R smash product to be regular multiplier Hopf algebras is given. In particular, the result of the paper implies Delvaux＇s main theorem in the case of smash products.展开更多
In order to study algebraic structures of parallelizable sphere s7, the notions of quasimodules and biquasimodnle algebras over Hopf quasigroups, which are not required to be associative, are introduced. The lack of a...In order to study algebraic structures of parallelizable sphere s7, the notions of quasimodules and biquasimodnle algebras over Hopf quasigroups, which are not required to be associative, are introduced. The lack of associativity of quasimodules is compensated for by conditions involving the antipode. The twisted smash product for Hopf quasigroups is constructed using biquasimodule algebras, which is a generalization of the twisted smash for Hopf algebras. The twisted smash product and tensor coproduct is turned into a Hopf quasigroup if and only if the following conditions （h1→a） h2 = （h2→a） h1, （a←S（h1）） h2 = （a←S（h2）） h1, hold. The obtained results generalize and improve the corresponding results of the twisted smash product for Hopf algebras.展开更多
Let k be a commutative ring, C a projective k-coalgebra. The smash productsof entwining structure (A, C)_ψ are discussed. When the map ψ is a bijective, and C is a finitelygenerated k-module, a version of the Ulbric...Let k be a commutative ring, C a projective k-coalgebra. The smash productsof entwining structure (A, C)_ψ are discussed. When the map ψ is a bijective, and C is a finitelygenerated k-module, a version of the Ulbrich theorem for coalgebras C is given.展开更多
This paper gives a sufficient and necessary condition for twisted products to be weak Hopf algebras, moreover, gives a description for smash products to be weak Hopf algebras. It respectively generalizes R.K.Molnar...This paper gives a sufficient and necessary condition for twisted products to be weak Hopf algebras, moreover, gives a description for smash products to be weak Hopf algebras. It respectively generalizes R.K.Molnar's major result and I.Boca's result.展开更多
基金Supported by the Ningbo Natural Science Foundation(2006A610089)
文摘The theory of L-R smash product is extended to multiplier Hopf algebras and a sufficient condition for L-R smash product to be regular multiplier Hopf algebras is given. In particular, the result of the paper implies Delvaux＇s main theorem in the case of smash products.
基金Supported by the Educational Ministry Science Technique Research Key Foundation of China(108154)the National Natural Science Foundation of China(10871170)
文摘This paper gives a duality theorem for weak L-R smash products,which extends the duality theorem for weak smash products given by Nikshych.
基金The National Natural Science Foundation of China( No. 10971188 )the Natural Science Foundation of Zhejiang Province(No.Y6110323)+2 种基金Jiangsu Planned Projects for Postdoctoral Research Funds(No. 0902081C)Zhejiang Provincial Education Department Project (No.Y200907995)Qiantang Talents Project of Science Technology Department of Zhejiang Province (No. 2011R10051)
文摘In order to study algebraic structures of parallelizable sphere s7, the notions of quasimodules and biquasimodnle algebras over Hopf quasigroups, which are not required to be associative, are introduced. The lack of associativity of quasimodules is compensated for by conditions involving the antipode. The twisted smash product for Hopf quasigroups is constructed using biquasimodule algebras, which is a generalization of the twisted smash for Hopf algebras. The twisted smash product and tensor coproduct is turned into a Hopf quasigroup if and only if the following conditions （h1→a） h2 = （h2→a） h1, （a←S（h1）） h2 = （a←S（h2）） h1, hold. The obtained results generalize and improve the corresponding results of the twisted smash product for Hopf algebras.
文摘Let k be a commutative ring, C a projective k-coalgebra. The smash productsof entwining structure (A, C)_ψ are discussed. When the map ψ is a bijective, and C is a finitelygenerated k-module, a version of the Ulbrich theorem for coalgebras C is given.
基金Supported by National Natural Science Foundation of China(10871170)Educational Minister Science Technology Key Foundation of China(10871170)College Special Research Doctoral Disciplines Point Fund of China(20100097110040)
基金This work is supported by National Natural Science Foundation of Chinaby the excellent doctorate fund of Nanjing agricultural university
文摘This paper gives a sufficient and necessary condition for twisted products to be weak Hopf algebras, moreover, gives a description for smash products to be weak Hopf algebras. It respectively generalizes R.K.Molnar's major result and I.Boca's result.
