Volume 4, Issue 1, June 2019, Page: 38-44
A Lot of Examples of Generalized Weak Bi-Frobenius Algebras
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
Received: Feb. 23, 2019;       Accepted: Apr. 4, 2019;       Published: Apr. 26, 2019
DOI: 10.11648/j.dmath.20190401.16      View  34      Downloads  8
Abstract
In this paper, by considering the tensor product of a bi-Frobenius algeba 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.
Keywords
Examples, Bi-Frobenius Algebras, Generalized Weak Bi-Frobenius Algebras
To cite this article
Yan Sun, Xiaohui Zhang, A Lot of Examples of Generalized Weak Bi-Frobenius Algebras, International Journal of Discrete Mathematics. Vol. 4, No. 1, 2019, pp. 38-44. doi: 10.11648/j.dmath.20190401.16
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
Y. Doi. Substructures of bi-Frobenius algebras. J. Algebra 256 (2), 568-582, 2002.
[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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