A Lot of Examples of Generalized Weak Bi-Frobenius Algebras

Yan Sun; Xiaohui Zhang

doi:doi:10.11648/j.dmath.20190401.16

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A Lot of Examples of Generalized Weak Bi-Frobenius Algebras

Yan Sun, Xiaohui Zhang

Published in International Journal of Discrete Mathematics (Volume 4, Issue 1)

Received: 23 February 2019 Accepted: 4 April 2019 Published: 26 April 2019

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Abstract

In this paper, by considering the tensor product of a bi-Frobenius algebra and a weak Hopf algebra, a lot of examples of the generalized weak bi-Frobenius algebras are given, such as the 16-dimensional, 24-dimensional and 40-dimensional GWBF algebras. They provide a common generalization of weak Hopf algebras introduced by Böhm, Nill, Szlachányi, and of bi-Frobenius algebras introduced by Doi and Takeuchi.

Published in	International Journal of Discrete Mathematics (Volume 4, Issue 1)
DOI	10.11648/j.dmath.20190401.16
Page(s)	38-44
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Examples, Bi-Frobenius Algebras, Generalized Weak Bi-Frobenius Algebras

References

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[2]	Y. Doi, M. Takeuchi. Bi-Frobenius algebras. New trends in Hopf algebra theory (La Falda, 1999), 67-97, Contemp. Math., 267, Amer. Math. Soc., Providence, RI, 2000.
[3]	Q. G. Chen, S. H. Wang. Radford’s formula for generalized weak biFrobenius algebras. Rocky Mountain J. Math. 44 (2), 419-433, 2014.
[4]	J. Bichon. The group of bi-Galois objects over the coordinate algebra of the Frobenius-Lusztig kernel of SL (2). Glasg. Math. J. 58 (3), 727-738, 2016.
[5]	Y. Y. Chen, L. Y. Zhang. The structure and construction of bi-Frobenius Hom-algebras. Comm. Algebra 45 (5), 2142-2162, 2017.
[6]	Z. H. Wang, L. B. Li. Double Frobenius algebras. Front. Math. China 13 (2), 399-415, 2018.
[7]	Y. H. Wang, X. W. Chen. Construct non-graded bi-Frobenius algebras via quivers. Sci. China Ser. A 50 (3), 450-456, 2007.
[8]	G. Böhm, F. Nill, K. Szlachányi. Weak Hopf Algebras - I. Integral Theory and C^* -Structure. J. Algebra 221, 385-438, 1999.
[9]	D. Nikshych. Semisimple weak Hopf algebras. J. Algebra 275 (2), 639-667, 2004.
[10]	D. Bulacu. A Clifford algebra is a weak Hopf algebra in a suitable symmetric monoidal category. J. Algebra 332, 244–284, 2011.
[11]	H. X. Zhu. The quantum double of a factorizable weak Hopf algebra. Comm. Algebra 45 (9), 4067-4083, 2017.
[12]	Y. H. Wang. Braided bi-Frobenius algebras. (Chinese) Chinese Ann. Math. Ser. A 28 (2), 203-214, 2007.
[13]	Y. H. Wang, P. Zhang. Construct bi-Frobenius algebras via quivers. Tsukuba J. Math. 28 (1), 215-221, 2004.
[14]	N. Yamatan. S4-formula and S2-formula for quasi-triangular bi-Frobenius algebras. Tsukuba J. Math. 26 (2), 339-349, 2002.
[15]	C. Kassel. Quantum Groups, Springer-Verlag, New York, 1995.

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Yan Sun, Xiaohui Zhang. (2019). A Lot of Examples of Generalized Weak Bi-Frobenius Algebras. International Journal of Discrete Mathematics, 4(1), 38-44. https://doi.org/10.11648/j.dmath.20190401.16

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ACS Style

Yan Sun; Xiaohui Zhang. A Lot of Examples of Generalized Weak Bi-Frobenius Algebras. Int. J. Discrete Math. 2019, 4(1), 38-44. doi: 10.11648/j.dmath.20190401.16

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AMA Style

Yan Sun, Xiaohui Zhang. A Lot of Examples of Generalized Weak Bi-Frobenius Algebras. Int J Discrete Math. 2019;4(1):38-44. doi: 10.11648/j.dmath.20190401.16

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@article{10.11648/j.dmath.20190401.16,
  author = {Yan Sun and Xiaohui Zhang},
  title = {A Lot of Examples of Generalized Weak Bi-Frobenius Algebras},
  journal = {International Journal of Discrete Mathematics},
  volume = {4},
  number = {1},
  pages = {38-44},
  doi = {10.11648/j.dmath.20190401.16},
  url = {https://doi.org/10.11648/j.dmath.20190401.16},
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  abstract = {In this paper, by considering the tensor product of a bi-Frobenius algebra and a weak Hopf algebra, a lot of examples of the generalized weak bi-Frobenius algebras are given, such as the 16-dimensional, 24-dimensional and 40-dimensional GWBF algebras. They provide a common generalization of weak Hopf algebras introduced by Böhm, Nill, Szlachányi, and of bi-Frobenius algebras introduced by Doi and Takeuchi.},
 year = {2019}
}

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TY  - JOUR
T1  - A Lot of Examples of Generalized Weak Bi-Frobenius Algebras
AU  - Yan Sun
AU  - Xiaohui Zhang
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T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
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AB  - In this paper, by considering the tensor product of a bi-Frobenius algebra and a weak Hopf algebra, a lot of examples of the generalized weak bi-Frobenius algebras are given, such as the 16-dimensional, 24-dimensional and 40-dimensional GWBF algebras. They provide a common generalization of weak Hopf algebras introduced by Böhm, Nill, Szlachányi, and of bi-Frobenius algebras introduced by Doi and Takeuchi.
VL  - 4
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Author Information

Yan Sun

School of Mathematical Sciences, Qufu Normal University, Qufu, The People's Republic of China
Xiaohui Zhang

School of Mathematical Sciences, Qufu Normal University, Qufu, The People's Republic of China

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Yan Sun, Xiaohui Zhang. (2019). A Lot of Examples of Generalized Weak Bi-Frobenius Algebras. International Journal of Discrete Mathematics, 4(1), 38-44. https://doi.org/10.11648/j.dmath.20190401.16

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ACS Style

Yan Sun; Xiaohui Zhang. A Lot of Examples of Generalized Weak Bi-Frobenius Algebras. Int. J. Discrete Math. 2019, 4(1), 38-44. doi: 10.11648/j.dmath.20190401.16

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AMA Style

Yan Sun, Xiaohui Zhang. A Lot of Examples of Generalized Weak Bi-Frobenius Algebras. Int J Discrete Math. 2019;4(1):38-44. doi: 10.11648/j.dmath.20190401.16

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@article{10.11648/j.dmath.20190401.16,
  author = {Yan Sun and Xiaohui Zhang},
  title = {A Lot of Examples of Generalized Weak Bi-Frobenius Algebras},
  journal = {International Journal of Discrete Mathematics},
  volume = {4},
  number = {1},
  pages = {38-44},
  doi = {10.11648/j.dmath.20190401.16},
  url = {https://doi.org/10.11648/j.dmath.20190401.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20190401.16},
  abstract = {In this paper, by considering the tensor product of a bi-Frobenius algebra and a weak Hopf algebra, a lot of examples of the generalized weak bi-Frobenius algebras are given, such as the 16-dimensional, 24-dimensional and 40-dimensional GWBF algebras. They provide a common generalization of weak Hopf algebras introduced by Böhm, Nill, Szlachányi, and of bi-Frobenius algebras introduced by Doi and Takeuchi.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - A Lot of Examples of Generalized Weak Bi-Frobenius Algebras
AU  - Yan Sun
AU  - Xiaohui Zhang
Y1  - 2019/04/26
PY  - 2019
N1  - https://doi.org/10.11648/j.dmath.20190401.16
DO  - 10.11648/j.dmath.20190401.16
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
SP  - 38
EP  - 44
PB  - Science Publishing Group
SN  - 2578-9252
UR  - https://doi.org/10.11648/j.dmath.20190401.16
AB  - In this paper, by considering the tensor product of a bi-Frobenius algebra and a weak Hopf algebra, a lot of examples of the generalized weak bi-Frobenius algebras are given, such as the 16-dimensional, 24-dimensional and 40-dimensional GWBF algebras. They provide a common generalization of weak Hopf algebras introduced by Böhm, Nill, Szlachányi, and of bi-Frobenius algebras introduced by Doi and Takeuchi.
VL  - 4
IS  - 1
ER  -

Copy | Download