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SOME RESULTS ABOUT HOM-COMODULE ALGEBRAS WITH HOM-HOPF MODULE STRUCTURE

Year 2019, Volume: 25 Issue: 25, 104 - 119, 08.01.2019
https://doi.org/10.24330/ieja.504128

Abstract

The main subject of this paper is Hom-comodule algebras with
Hom-Hopf module structure. First, we give the factorization of a class of Hom-
bialgebras, which is not only Hom-module coalgebras but also Hom-comodule
algebras with Hom-Hopf module structure. Next, we obtain the factorization of
this class of Hom-comodule algebras. Finally, we discuss the relation between
this class of Hom-comodule algebas and cleft extensions.

References

  • R. J. Blattner, M. Cohen and S. Montgomery, Crossed products and inner actions of Hopf algebras, Trans. Amer. Math. Soc., 298(2) (1986), 671-711.
  • R. J. Blattner and S. Montgomery, Crossed products and Galois extensions of Hopf algebras, Paci c J. Math., 137(1) (1989), 37-54.
  • L. H. Dong, S. Xue and X. Zhang, The factorization for a class of Hom- coalgebras, Adv. Math. Phys., (2017), 4653172 (14 pp).
  • J. T. Hartwig, D. Larsson and S. D. Silvestrov, Deformations of Lie algebras using -derivations, J. Algebra, 295(2) (2006), 314-361.
  • D. W. Lu and S. H. Wang, Crossed product Hom-Hopf algebras and lazy 2- cocycle, arXiv: 1509.01518v2.
  • T. S. Ma H. Y. Li and T. Yang, Cobraided smash product Hom-Hopf algebras, Colloq. Math., 134(1) (2014), 75-92.
  • A. Makhlouf and S. D. Silvestrov, Hom-algebra structures, J. Gen. Lie Theory Appl., 2(2) (2008), 51-64.
  • A. Makhlouf and S. D. Silvestrov, Hom-algebras and Hom-coalgebras, J. Alge- bra Appl., 9(4) (2010), 553-589.
  • 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 Amer. Math. Soc., Providence, RI, 1993.
  • D. Yau, Hom-bialgebras and comodule Hom-algebras, Int. Electron. J. Algebra, 8 (2010), 45-64.
Year 2019, Volume: 25 Issue: 25, 104 - 119, 08.01.2019
https://doi.org/10.24330/ieja.504128

Abstract

References

  • R. J. Blattner, M. Cohen and S. Montgomery, Crossed products and inner actions of Hopf algebras, Trans. Amer. Math. Soc., 298(2) (1986), 671-711.
  • R. J. Blattner and S. Montgomery, Crossed products and Galois extensions of Hopf algebras, Paci c J. Math., 137(1) (1989), 37-54.
  • L. H. Dong, S. Xue and X. Zhang, The factorization for a class of Hom- coalgebras, Adv. Math. Phys., (2017), 4653172 (14 pp).
  • J. T. Hartwig, D. Larsson and S. D. Silvestrov, Deformations of Lie algebras using -derivations, J. Algebra, 295(2) (2006), 314-361.
  • D. W. Lu and S. H. Wang, Crossed product Hom-Hopf algebras and lazy 2- cocycle, arXiv: 1509.01518v2.
  • T. S. Ma H. Y. Li and T. Yang, Cobraided smash product Hom-Hopf algebras, Colloq. Math., 134(1) (2014), 75-92.
  • A. Makhlouf and S. D. Silvestrov, Hom-algebra structures, J. Gen. Lie Theory Appl., 2(2) (2008), 51-64.
  • A. Makhlouf and S. D. Silvestrov, Hom-algebras and Hom-coalgebras, J. Alge- bra Appl., 9(4) (2010), 553-589.
  • 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 Amer. Math. Soc., Providence, RI, 1993.
  • D. Yau, Hom-bialgebras and comodule Hom-algebras, Int. Electron. J. Algebra, 8 (2010), 45-64.
There are 10 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Lihong Dong This is me

Shuan Xue This is me

Publication Date January 8, 2019
Published in Issue Year 2019 Volume: 25 Issue: 25

Cite

APA Dong, L., & Xue, S. (2019). SOME RESULTS ABOUT HOM-COMODULE ALGEBRAS WITH HOM-HOPF MODULE STRUCTURE. International Electronic Journal of Algebra, 25(25), 104-119. https://doi.org/10.24330/ieja.504128
AMA Dong L, Xue S. SOME RESULTS ABOUT HOM-COMODULE ALGEBRAS WITH HOM-HOPF MODULE STRUCTURE. IEJA. January 2019;25(25):104-119. doi:10.24330/ieja.504128
Chicago Dong, Lihong, and Shuan Xue. “SOME RESULTS ABOUT HOM-COMODULE ALGEBRAS WITH HOM-HOPF MODULE STRUCTURE”. International Electronic Journal of Algebra 25, no. 25 (January 2019): 104-19. https://doi.org/10.24330/ieja.504128.
EndNote Dong L, Xue S (January 1, 2019) SOME RESULTS ABOUT HOM-COMODULE ALGEBRAS WITH HOM-HOPF MODULE STRUCTURE. International Electronic Journal of Algebra 25 25 104–119.
IEEE L. Dong and S. Xue, “SOME RESULTS ABOUT HOM-COMODULE ALGEBRAS WITH HOM-HOPF MODULE STRUCTURE”, IEJA, vol. 25, no. 25, pp. 104–119, 2019, doi: 10.24330/ieja.504128.
ISNAD Dong, Lihong - Xue, Shuan. “SOME RESULTS ABOUT HOM-COMODULE ALGEBRAS WITH HOM-HOPF MODULE STRUCTURE”. International Electronic Journal of Algebra 25/25 (January 2019), 104-119. https://doi.org/10.24330/ieja.504128.
JAMA Dong L, Xue S. SOME RESULTS ABOUT HOM-COMODULE ALGEBRAS WITH HOM-HOPF MODULE STRUCTURE. IEJA. 2019;25:104–119.
MLA Dong, Lihong and Shuan Xue. “SOME RESULTS ABOUT HOM-COMODULE ALGEBRAS WITH HOM-HOPF MODULE STRUCTURE”. International Electronic Journal of Algebra, vol. 25, no. 25, 2019, pp. 104-19, doi:10.24330/ieja.504128.
Vancouver Dong L, Xue S. SOME RESULTS ABOUT HOM-COMODULE ALGEBRAS WITH HOM-HOPF MODULE STRUCTURE. IEJA. 2019;25(25):104-19.