Abstract
Using the quiver technique we construct a class of non-graded bi-Frobenius algebras. We also classify a class of graded bi-Frobenius algebras via certain equations of structure coefficients.
Similar content being viewed by others
References
Chen X W, Huang H L, Wang Y H. A note on modules, comodules and cotensor products over Frobenius algebras. Chin Ann Math Ser B, 27(4): 419–424 (2006)
Doi Y, Takeuchi M. Bi-Frobenius algebras. Contemp Math, AMS, 267: 67–97 (2002)
Doi Y. Bi-Frobenius algebras and group-like algebras. In: Hopf Algebras. Lecture Notes in Pure and Appl Math, Vol. 237. New York: Dekker, 2004. 143–155
Auslander M, Reiten I, Smalø S O. Representation Theory of Artin Algebras. Cambridge Studies in Adv Math 36. Cambridge: Cambridge Univ Press, 1995
Chen X W, Huang H L, Ye Y, Zhang P. Monomial Hopf algebras. J Algebra, 275: 212–232 (2004)
Chen X W, Huang H L, Zhang P. Dual Gabriel Theorem with applications. Sci China Ser A-Math, 49(1): 9–26 (2006)
Chin W, Montgomery S. Basic coalgebras, Modular interfaces (Reverside, CA). 1995, 41–47, AMS/IP Stud Adv Math 4. Providence: Amer Math Soc, 1997
Wang Y H, Zhang P. Construct bi-Frobenius algebras via quivers. Tsukuba J Math, 28(1): 215–221 (2004)
Gerstenhaber M. Deformations of rings and algebras. Ann Math, 79(2): 59–103 (1964)
Braverman A, Gaitsgory D. Poincaré-Birkhoff-Witt theorem for quadratic algebras of Koszul type. J Algebra, 181: 315–328 (1996)
Schneider H J. Lectures on Hopf algebras. Córdoba: University of Argentina, 1995. 52
Liu G X, Ye Y. Monomial Hopf algebras over fields of positive characteristic. Sci China Ser A-Math, 49(3): 320–329 (2006)
Dǎscǎlescu S, Nǎstǎsescu C, Raianu S. Hopf Algebras: An Introduction. New York-Basel: Marcel Dekker, 2000
Doi Y. Substructures of bi-Frobenius algebras. J Algebra, 256: 568–582 (2002)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 10501041, 10271113, 10601052)
Rights and permissions
About this article
Cite this article
Wang, Yh., Chen, Xw. Construct non-graded bi-Frobenius algebras via quivers. SCI CHINA SER A 50, 450–456 (2007). https://doi.org/10.1007/s11425-007-2035-7
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11425-007-2035-7