Relative HomHopf modules and total integrals
Abstract
Let (H, α) be a monoidal HomHopf algebra and (A, β) a right (H, α)Homcomodule algebra. We first investigate the criterion for the existence of a total integral of (A, β) in the setting of monoidal HomHopf algebras. Also, we prove that there exists a total integral ϕ : (H, α) → (A, β) if and only if any representation of the pair (H, A) is injective in a functorial way, as a corepresentation of (H, α), which generalizes Doi’s result. Finally, we define a total quantum integral γ : H → Hom(H, A) and prove the following affineness criterion: if there exists a total quantum integral γ and the canonical map ψ : A⊗{sub B}A → A ⊗ H, a⊗{sub B}b ↦ β{sup −1}(a) b{sub [0]} ⊗ α(b{sub [1]}) is surjective, then the induction functor A⊗{sub B}−:ℋ{sup ~}(ℳ{sub k}){sub B}→ℋ{sup ~}(ℳ{sub k}){sub A}{sup H} is an equivalence of categories.
 Authors:
 School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025 (China)
 Department of Mathematics, Southeast University, Nanjing 210096 (China)
 School of Mathematics and Finance, Chuzhou University, Chuzhou 239000 (China)
 (China)
 Publication Date:
 OSTI Identifier:
 22403093
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; INDUCTION; INTEGRALS; MATHEMATICAL OPERATORS; QUANTUM GROUPS
Citation Formats
Guo, Shuangjian, Zhang, Xiaohui, Wang, Shengxiang, Email: wangsxmath@163.com, and Department of Mathematics, Nanjing University, Nanjing 210093. Relative HomHopf modules and total integrals. United States: N. p., 2015.
Web. doi:10.1063/1.4906938.
Guo, Shuangjian, Zhang, Xiaohui, Wang, Shengxiang, Email: wangsxmath@163.com, & Department of Mathematics, Nanjing University, Nanjing 210093. Relative HomHopf modules and total integrals. United States. doi:10.1063/1.4906938.
Guo, Shuangjian, Zhang, Xiaohui, Wang, Shengxiang, Email: wangsxmath@163.com, and Department of Mathematics, Nanjing University, Nanjing 210093. 2015.
"Relative HomHopf modules and total integrals". United States.
doi:10.1063/1.4906938.
@article{osti_22403093,
title = {Relative HomHopf modules and total integrals},
author = {Guo, Shuangjian and Zhang, Xiaohui and Wang, Shengxiang, Email: wangsxmath@163.com and Department of Mathematics, Nanjing University, Nanjing 210093},
abstractNote = {Let (H, α) be a monoidal HomHopf algebra and (A, β) a right (H, α)Homcomodule algebra. We first investigate the criterion for the existence of a total integral of (A, β) in the setting of monoidal HomHopf algebras. Also, we prove that there exists a total integral ϕ : (H, α) → (A, β) if and only if any representation of the pair (H, A) is injective in a functorial way, as a corepresentation of (H, α), which generalizes Doi’s result. Finally, we define a total quantum integral γ : H → Hom(H, A) and prove the following affineness criterion: if there exists a total quantum integral γ and the canonical map ψ : A⊗{sub B}A → A ⊗ H, a⊗{sub B}b ↦ β{sup −1}(a) b{sub [0]} ⊗ α(b{sub [1]}) is surjective, then the induction functor A⊗{sub B}−:ℋ{sup ~}(ℳ{sub k}){sub B}→ℋ{sup ~}(ℳ{sub k}){sub A}{sup H} is an equivalence of categories.},
doi = {10.1063/1.4906938},
journal = {Journal of Mathematical Physics},
number = 2,
volume = 56,
place = {United States},
year = 2015,
month = 2
}

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