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THE STRUCTURE THEOREM OF HOM-HOPF BIMODULES AND ITS APPLICATIONS

Year 2021, , 78 - 98, 17.07.2021
https://doi.org/10.24330/ieja.969590

Abstract

In this paper, we give the structure theorem of Hom-Hopf bimodules. Furthermore, we give the structure theorem of Hom-comodule algebras.
Finally, we consider and study the structure theorems of Hom-Hopf bicomodules and Hom-module coalgebras.

References

  • Y. Bespalov and B. Drabant, Hopf (bi-)modules and crossed modules in braided monoidal categories, J. Pure Appl. Algebra, 123(1-3) (1998), 105-129.
  • T. Brzezinski and R. Wisbauer, Corings and Comodules, London Mathematical Society Lecture Note Series, 309, Cambridge University Press, Cambridge, 2003.
  • S. Caenepeel and I. Goyvaerts, Monoidal Hom-Hopf algebras, Comm. Algebra, 39(6) (2011), 2216-2240.
  • Y. Y. Chen, Z. W. Wang and L. Y. Zhang, Integrals for monoidal Hom-Hopf algebras and their applications, J. Math. Phys., 54(7) (2013), 073515 (22 pp).
  • Y. Y. Chen, Z. W. Wang and L. Y. Zhang, The fundamental theorem and Maschke's theorem in the category of relative Hom-Hopf modules, Colloq. Math., 144(1) (2016), 55-71.
  • Y. Y. Chen and L. Y. Zhang, The category of Yetter-Drinfel'd Hom-modules and the quantum Hom-Yang-Baxter equation, J. Math. Phys., 55(3) (2014), 031702 (18 pp).
  • Y. Y. Chen, H. H. Zheng and L. Y. Zhang, Double Hom-associative algebra and double Hom-Lie bialgebra, Adv. Appl. Cli ord Algebr., 30(1) (2020), Paper No. 8 (25 pp).
  • S. Dascalescu, C. Nastasescu and S. Raianu, Hopf Algebras: An Introduction, Monographs and Textbooks in Pure and Applied Mathematics, 235, Marcel- Dekker, Inc., New York, 2001.
  • J. Dello, F. Panaite, F. Van Oystaeyen and Y. Zhang, Structure theorems for bicomodule algebras over quasi-Hopf algebras, weak Hopf algebras, and braided Hopf algebras, Comm. Algebra, 44(11) (2016), 4609-4636.
  • J. T. Hartwig, D. Larsson and S. D. Silvestrov, Deformations of Lie algebras using $\sigma$-derivations, J. Algebra, 295(2) (2006), 314-361.
  • F. Hausser and F. Nill, Integral theory for quasi-Hopf algebras, (1999), arXiv:math/9904164.
  • R. G. Larson and M. E. Sweedler, An associative orthogonal bilinear form for Hopf algebras, Amer. J. Math., 91(1) (1969), 75-94.
  • H. Li and T. Ma, A construction of the Hom-Yetter-Drinfeld category, Colloq. Math., 137(1) (2014), 43-65.
  • L. Liu and B. Shen, Radford's biproducts and Yetter-Drinfeld modules for monoidal Hom-Hopf algebras, J. Math. Phys., 55(3) (2014), 031701 (16 pp).
  • A. Makhlouf and F. Panaite, Yetter-Drinfeld modules for Hom-bialgebras, J. Math. Phys., 55(1) (2014), 013501 (17 pp).
  • G. Militaru and D. Stefan, Extending modules for Hopf Galois extensions, Comm. Algebra, 22(14) (1994), 5657-5678.
  • S. Montgomery, Hopf Algebras and Their Actions on Rings, CBMS Regional Conference Series in Mathematics, 82, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1993.
  • R. F. Niu, Y. Wang and L. Y. Zhang, The structure theorem of endomorphism algebras for weak Doi-Hopf modules, Acta Math. Hungar., 127(3) (2010), 273- 290.
  • P. Saracco, On the structure theorem for quasi-Hopf bimodules, Appl. Categ. Structures, 25(1) (2017), 3-28.
  • P. Schauenburg, Bialgebras over noncommutative rings and a structure theorem for Hopf bimodules, Appl. Categ. Structures, 6(2) (1998), 193-222.
  • M. E. Sweedler, Hopf Algebras, Mathematics Lecture Note Series W. A. Benjamin, Inc., New York, 1969.
  • Y. Wang and L. Y. Zhang, The structure theorem for weak module coalgebras, Math. Notes, 88(1-2) (2010), 3-15.
  • D. Yau, Hom-quantum groups I: quasi-triangular Hom-bialgebras, J. Phys. A, 45(6) (2012), 065203 (23 pp).
  • L. Y. Zhang, The Structure theorem of weak comodule algebras, Comm. Algebra, 38(1) (2010), 254-260.
Year 2021, , 78 - 98, 17.07.2021
https://doi.org/10.24330/ieja.969590

Abstract

References

  • Y. Bespalov and B. Drabant, Hopf (bi-)modules and crossed modules in braided monoidal categories, J. Pure Appl. Algebra, 123(1-3) (1998), 105-129.
  • T. Brzezinski and R. Wisbauer, Corings and Comodules, London Mathematical Society Lecture Note Series, 309, Cambridge University Press, Cambridge, 2003.
  • S. Caenepeel and I. Goyvaerts, Monoidal Hom-Hopf algebras, Comm. Algebra, 39(6) (2011), 2216-2240.
  • Y. Y. Chen, Z. W. Wang and L. Y. Zhang, Integrals for monoidal Hom-Hopf algebras and their applications, J. Math. Phys., 54(7) (2013), 073515 (22 pp).
  • Y. Y. Chen, Z. W. Wang and L. Y. Zhang, The fundamental theorem and Maschke's theorem in the category of relative Hom-Hopf modules, Colloq. Math., 144(1) (2016), 55-71.
  • Y. Y. Chen and L. Y. Zhang, The category of Yetter-Drinfel'd Hom-modules and the quantum Hom-Yang-Baxter equation, J. Math. Phys., 55(3) (2014), 031702 (18 pp).
  • Y. Y. Chen, H. H. Zheng and L. Y. Zhang, Double Hom-associative algebra and double Hom-Lie bialgebra, Adv. Appl. Cli ord Algebr., 30(1) (2020), Paper No. 8 (25 pp).
  • S. Dascalescu, C. Nastasescu and S. Raianu, Hopf Algebras: An Introduction, Monographs and Textbooks in Pure and Applied Mathematics, 235, Marcel- Dekker, Inc., New York, 2001.
  • J. Dello, F. Panaite, F. Van Oystaeyen and Y. Zhang, Structure theorems for bicomodule algebras over quasi-Hopf algebras, weak Hopf algebras, and braided Hopf algebras, Comm. Algebra, 44(11) (2016), 4609-4636.
  • J. T. Hartwig, D. Larsson and S. D. Silvestrov, Deformations of Lie algebras using $\sigma$-derivations, J. Algebra, 295(2) (2006), 314-361.
  • F. Hausser and F. Nill, Integral theory for quasi-Hopf algebras, (1999), arXiv:math/9904164.
  • R. G. Larson and M. E. Sweedler, An associative orthogonal bilinear form for Hopf algebras, Amer. J. Math., 91(1) (1969), 75-94.
  • H. Li and T. Ma, A construction of the Hom-Yetter-Drinfeld category, Colloq. Math., 137(1) (2014), 43-65.
  • L. Liu and B. Shen, Radford's biproducts and Yetter-Drinfeld modules for monoidal Hom-Hopf algebras, J. Math. Phys., 55(3) (2014), 031701 (16 pp).
  • A. Makhlouf and F. Panaite, Yetter-Drinfeld modules for Hom-bialgebras, J. Math. Phys., 55(1) (2014), 013501 (17 pp).
  • G. Militaru and D. Stefan, Extending modules for Hopf Galois extensions, Comm. Algebra, 22(14) (1994), 5657-5678.
  • S. Montgomery, Hopf Algebras and Their Actions on Rings, CBMS Regional Conference Series in Mathematics, 82, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1993.
  • R. F. Niu, Y. Wang and L. Y. Zhang, The structure theorem of endomorphism algebras for weak Doi-Hopf modules, Acta Math. Hungar., 127(3) (2010), 273- 290.
  • P. Saracco, On the structure theorem for quasi-Hopf bimodules, Appl. Categ. Structures, 25(1) (2017), 3-28.
  • P. Schauenburg, Bialgebras over noncommutative rings and a structure theorem for Hopf bimodules, Appl. Categ. Structures, 6(2) (1998), 193-222.
  • M. E. Sweedler, Hopf Algebras, Mathematics Lecture Note Series W. A. Benjamin, Inc., New York, 1969.
  • Y. Wang and L. Y. Zhang, The structure theorem for weak module coalgebras, Math. Notes, 88(1-2) (2010), 3-15.
  • D. Yau, Hom-quantum groups I: quasi-triangular Hom-bialgebras, J. Phys. A, 45(6) (2012), 065203 (23 pp).
  • L. Y. Zhang, The Structure theorem of weak comodule algebras, Comm. Algebra, 38(1) (2010), 254-260.
There are 24 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Huihui Zheng This is me

Yuanyuan Chen This is me

Liangyun Zhang This is me

Publication Date July 17, 2021
Published in Issue Year 2021

Cite

APA Zheng, H., Chen, Y., & Zhang, L. (2021). THE STRUCTURE THEOREM OF HOM-HOPF BIMODULES AND ITS APPLICATIONS. International Electronic Journal of Algebra, 30(30), 78-98. https://doi.org/10.24330/ieja.969590
AMA Zheng H, Chen Y, Zhang L. THE STRUCTURE THEOREM OF HOM-HOPF BIMODULES AND ITS APPLICATIONS. IEJA. July 2021;30(30):78-98. doi:10.24330/ieja.969590
Chicago Zheng, Huihui, Yuanyuan Chen, and Liangyun Zhang. “THE STRUCTURE THEOREM OF HOM-HOPF BIMODULES AND ITS APPLICATIONS”. International Electronic Journal of Algebra 30, no. 30 (July 2021): 78-98. https://doi.org/10.24330/ieja.969590.
EndNote Zheng H, Chen Y, Zhang L (July 1, 2021) THE STRUCTURE THEOREM OF HOM-HOPF BIMODULES AND ITS APPLICATIONS. International Electronic Journal of Algebra 30 30 78–98.
IEEE H. Zheng, Y. Chen, and L. Zhang, “THE STRUCTURE THEOREM OF HOM-HOPF BIMODULES AND ITS APPLICATIONS”, IEJA, vol. 30, no. 30, pp. 78–98, 2021, doi: 10.24330/ieja.969590.
ISNAD Zheng, Huihui et al. “THE STRUCTURE THEOREM OF HOM-HOPF BIMODULES AND ITS APPLICATIONS”. International Electronic Journal of Algebra 30/30 (July 2021), 78-98. https://doi.org/10.24330/ieja.969590.
JAMA Zheng H, Chen Y, Zhang L. THE STRUCTURE THEOREM OF HOM-HOPF BIMODULES AND ITS APPLICATIONS. IEJA. 2021;30:78–98.
MLA Zheng, Huihui et al. “THE STRUCTURE THEOREM OF HOM-HOPF BIMODULES AND ITS APPLICATIONS”. International Electronic Journal of Algebra, vol. 30, no. 30, 2021, pp. 78-98, doi:10.24330/ieja.969590.
Vancouver Zheng H, Chen Y, Zhang L. THE STRUCTURE THEOREM OF HOM-HOPF BIMODULES AND ITS APPLICATIONS. IEJA. 2021;30(30):78-9.