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Advances in Mathematical Physics
Volume 2017 (2017), Article ID 4653172, 14 pages
https://doi.org/10.1155/2017/4653172
Research Article

The Factorization for a Class of Hom-Coalgebras

1College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
2School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Correspondence should be addressed to Lihong Dong

Received 15 May 2017; Revised 10 August 2017; Accepted 7 September 2017; Published 29 October 2017

Academic Editor: Yao-Zhong Zhang

Copyright © 2017 Lihong Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Makhlouf and S. D. Silvestrov, “Hom-algebra structures,” Journal of Generalized Lie Theory and Applications, vol. 2, no. 2, pp. 51–64, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  2. A. Makhlouf and S. Silvestrov, “Hom-algebras and Hom-coalgebras,” Journal of Algebra and Its Applications, vol. 9, no. 4, pp. 553–589, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. R. J. Blattner, M. Cohen, and S. Montgomery, “Crossed products and inner actions of Hopf algebras,” Transactions of the American Mathematical Society, vol. 298, no. 2, pp. 671–711, 1986. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. Y. Doi and M. Takeuchi, “Cleft comodule algebras for a bialgebra,” Communications in Algebra, vol. 14, no. 5, pp. 801–817, 1986. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. R. J. Blattner and S. Montgomery, “Crossed products and Galois extensions of Hopf algebras,” Pacific Journal of Mathematics, vol. 137, no. 1, pp. 37–54, 1989. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. D. W. Lu and S. H. Wang, “Crossed product Hom-Hopf algebras and lazy 2-cocycle,” https://arxiv.org/pdf/1509.01518.pdf.
  7. S. Caenepeel, S. Dascalescu, and S. Raianu, “A Maschke-type theorem for crossed coproclucts,” An. Stiint. Univ. Ovidius Constanta Ser. Mat, vol. 2, pp. 44–51, 1994. View at Google Scholar · View at MathSciNet
  8. S. Dascalescu, G. Militaru, and S. Raianu, “Crossed coproducts and cleft coextensions,” Communications in Algebra, vol. 24, no. 4, pp. 1229–1243, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  9. S. Dascalescu, S. Raianu, and Y. H. Zhang, “Finite Hopf-Galois coextensions, crossed coproducts, and duality,” Journal of Algebra, vol. 178, no. 2, pp. 400–413, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  10. D. E. Radford, “The structure of Hopf algebras with a projection,” Journal of Algebra, vol. 92, no. 2, pp. 322–347, 1985. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. S. Caenepeel, B. Ion, G. Militaru, and S. Zhu, “The factorization problem and the smash biproduct of algebras and coalgebras,” Algebras and Representation Theory, vol. 3, no. 1, pp. 19–42, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. S. Guo and X.-L. Chen, “A Maschke type theorem for relative Hom-HOPf modules,” Czechoslovak Mathematical Journal, vol. 64(139), no. 3, pp. 783–799, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. D. Yau, “Enveloping algebras of Hom-Lie algebras,” Journal of Generalized Lie Theory and Applications, vol. 2, no. 2, pp. 95–108, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  14. D. Yau, “Hom-bialgebras and comodule Hom-algebras,” International Electronic Journal of Algebra, vol. 8, pp. 45–64, 2010. View at Google Scholar · View at MathSciNet
  15. T. Ma, H. Li, and T. Yang, “Cobraided smash product Hom-HOPf algebras,” Colloquium Mathematicum, vol. 134, no. 1, pp. 75–92, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. A. Masuoka and Y. Doi, “Generalization of cleft comodule algebras,” Communications in Algebra, vol. 20, no. 12, pp. 3703–3721, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus