Integrals for monoidal Hom-Hopf algebras and their applications
Integrals for monoidal Hom-Hopf algebras and their applications
复制标题
DOI：
10.1063/1.4813447
复制
发表时间：
2013-07
影响因子：
1.3
通讯作者：
Yuan-yuan Chen;Zhong-wei Wang;Liangyun Zhang
中科院分区：
文献类型：
--
作者：
Yuan-yuan Chen;Zhong-wei Wang;Liangyun Zhang
引入了Monoidal Hom-Hopf代数的积分概念，研究了有限维Monoidal Hom-Hopf代数积分的存在唯一性。然后将积分应用到Monoidal Hom-Hopf代数的Maschke型定理中，控制Monoidal Hom-Hopf代数的半单性和可分性。进一步，刻画了Monoidal Hom-Hopf代数具有额外的Frobenius性质，并研究了有限维Monoidal Hom-Hopf代数何时是Frobenius的问题。作为积分的应用，给出了Hom-smash积的Maschke型定理，并构造了Hom-范畴H（Mk）中的Morita上下文.
Integrals of monoidal Hom-Hopf algebras are introduced and the existence and uniqueness of integrals for finite-dimensional monoidal Hom-Hopf algebras are investigated first. Then integrals are applied to the Maschke type theorem for monoidal Hom-Hopf algebras controlling the semisimplicity and separability of monoidal Hom-Hopf algebras. Further, monoidal Hom-algebras are characterized with additional Frobenius property, and the question when finite-dimensional monoidal Hom-Hopf algebras are Frobenius is studied. As applications of integrals, the Maschke type theorem for Hom-smash product is given, and the Morita context in the Hom-category H(Mk) is constructed.