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Long Bialgebras, Dimodule Algebras and Quantum Yang–Baxter Modules over Long Bialgebras

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Abstract

This paper gives a sufficient and necessary condition for a bialgebra to be a Long bialgebra, and proves a braided product to be a Long bialgebra under some conditions. It also gives a direct sum decomposition of quantum Yang–Baxter modules over Long bialgebras.

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References

  1. Militaru, G.: A class of non–symmetric solutions for the integrability condition of the Knizhnik–Zamolodchikov equation: a Hopf algebra approach. Comm. Algebra, 27(5), 2393–2407 (1999)

    MATH  MathSciNet  Google Scholar 

  2. Caenepeel, S., Oystaeyen, F. V., Zhang, Y. H.: Quantum Yang–Baxter module algebras. K–Theory, 8, 231–255 (1994)

    MATH  MathSciNet  Google Scholar 

  3. Doi, Y.: Braided bialgebras and quadratic bialgebras. Comm. Algebra, 21(5), 1731–1749 (1993)

    MATH  MathSciNet  Google Scholar 

  4. Kauffman, L., Radford, D.E.: Quantum algebras, quantum coalgbras, invariants of 1–1 tangles and knots. Comm. Algebra, 28(11), 5101–5156 (2000)

    MATH  MathSciNet  Google Scholar 

  5. Montgomery, S.: Hopf algebras and their actions on rings, CBMS, Lect. Notes, 82, 1993

  6. Zhu, J. G.: Cosemisimple coextensions and homological dimension of smash coproducts. Acta Mathematica Sinica, English Series, 21(3), 563–568 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bahturin, Y., Fischman, D., Montgomery, S.: Bicharacters, twistings, and Scheunert’s theorem for Hopf algebras. J. Algebra, 236, 246–276 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  8. Zhang, L. Y., Tong, W. T.: Quantum Yang–Baxter H–module algebras and their braided products. Comm. Algebra, 31(5), 2471–2495 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Li, F.: On Quasi–bicrossed products of weak Hopf algebras. Acta Mathematica Sinica, English Series, 20(2), 305–318 (2004)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. College of Science, Nanjing Agricultural University, Nanjing 210095, P. R. China

    Liang Yun Zhang

  2. Department of Mathematics, Nanjing University, Nanjing 210008, P. R. China

    Liang Yun Zhang

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  1. Liang Yun Zhang
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Correspondence to Liang Yun Zhang.

Additional information

Supported by National Natural Science Foundation of P. R. China No. 10571153 and Post-Doctoral Program of P. R. China, No. 2005037713, and Post–Doctoral Program of Jiangsu Province of China No. 0203003403 and National Science Foundation of Jiangsu Province of China No. 04KJB110051

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Zhang, L.Y. Long Bialgebras, Dimodule Algebras and Quantum Yang–Baxter Modules over Long Bialgebras. Acta Math Sinica 22, 1261–1270 (2006). https://doi.org/10.1007/s10114-005-0683-5

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  • DOI: https://doi.org/10.1007/s10114-005-0683-5

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