Abstract
The notion of a Hopf algebra was developed by algebraic topologists abstracting the work of H.Hopf on manifolds in 1941.In this paper, we mainly study a right twisted smash product A*H over weak Hopf algebras and investigate their properties.The concet of a right twisted smash product algebras over weak Hopf akgebras is constructed. Let H be a weak Hopf algebra and A an H-module algebra,we give a sufficient and necessary condition for a right twisted smash product A*H to be a weak bialgebra . Simultaneously,we also give a sufficient condition for A*H to be a weak Hopf algebra.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bohm, G., Nill, F., Szlachanyi, K.: Weak Hopf Algebras I: Integral Theory and C* structure. J. Algebra, 385 (1999)
Sweedler, M.E.: Hopf Algebras, Berjamin, New York (1969)
Hirata, K., Sugano, K.: On Semisimple extensions and separable extensions over non commutative rings. J.Math. Soc. Japan 18(4), 360–373 (1966)
Cohen, M., Fishman, D.: Hopf algebra actions. J. Algebra 10, 363–379 (1986)
Wang, S., Li, J.q.: On Twisted Smash Products for Bimodules Algebras and the Drinfel‘d Double. Comm. Algebra 26, 2435–2444 (1998)
Zheng, N.: Smash Biproduct Over Weak Hopf Algebras. Advances in Mathematics (05) (2009)
Shi, M.: The Complexity of Smash product. Advances in Mathematics (05) (2008)
Jiao, Z., Li, J.: The L-R Weak Smash Product over Weak Hopf Algbras, vol. (01) (2009)
Ling, J.: Maschke-Type Therems for Weak Smash Coproducts. Journal of Mathematical Re-Search and Exposition (04) (2009)
Yin, Y., Zhang, M.: The Structure Theorem for Weak Hopf Algebras. Advances in Mathematics  (06) (2009)
Ju, T.: Cocyclic Module Constructed By The Right Adjoint Action Of Hopf Algebras. Journal of Mathematics (02) (2010)
Ju, T.: Cocyclic Module Constructed By The Right Adjoint Action of Hopf Algebras. Journal of Mathematics (02) (2010)
Ju, T.: The cotwists for Hopf algebras. Journal of Natural Science of Heilongjiang University (01) (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yan, Y., Ma, X., Li, D., Du, L., Li, Y. (2011). A*H over Weak Hopf Algebras. In: Liu, C., Chang, J., Yang, A. (eds) Information Computing and Applications. ICICA 2011. Communications in Computer and Information Science, vol 244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27452-7_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-27452-7_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27451-0
Online ISBN: 978-3-642-27452-7
eBook Packages: Computer ScienceComputer Science (R0)