# Hom-Hopf代数上的交叉余积Crossed Coproducts over Hom-Hopf Algebras

Abstract: In order to study the Hom-crossed-coproduct, we define the Hom-crossed-coproduct by analogy, and give some properties of Hom-crossed-coproduct by calculation. As an application, we obtain the necessary and sufficient conditions for Hom-crossed- coproduct to form Hom-coalgebra, and the necessary and sufficient conditions for Hom-crossed-coproduct and Hom-smash-product to form Hom-bialgebra.

[1] Hu, N.H. (1999) Q-Witt Algebras, q-Lie Algebras, q-Holomorph Structure and Representa- tions. Algebra Colloquium, 6, 51-70.

[2] Aizawa, N. and Sato, H. (1991) Q-Deformation of the Virasoro Algebra with Central Extension.Physics Letters B, 256, 185-190.
https://doi.org/10.1016/0370-2693(91)90671-C

[3] Makhlouf, A. and Silvestrov, S. (2008) Hom-Algebras Structures. Journal of Generalized Lie Theory and Applications, 2, 51-64.
https://doi.org/10.4303/jglta/S070206

[4] Makhlouf, A. and Silvestrov, S. (2010) Hom-Algebras and Hom-Coalgebras. Journal of Algebra and Its Applications, 9, 553-589.
https://doi.org/10.1142/S0219498810004117

[5] Caenepeel, S. and Goyvaerts, I. (2011) Monoidal Hom-Hopf Algebras. Communications in Algebra, 39, 2216-2240.
https://doi.org/10.1080/00927872.2010.490800

[6] Makhlouf, A. and Silvestrov, S. (2007) Hom-Lie Admissible Hom-Coalgebras and Hom-Hopf Algebras. Non-Commutative Geometry, 81, 189-206.

[7] Yau, D. (2010) Hom-Bialgebras and Comodule Hom-Algebras. International Electronic Journal of Algebra, 8, 45-64.

[8] Wang, S.H., Chen, L.Y., Jiao, Z.M. and Zhao, W.Z. (1996) Hopf Algebra Structures on Crossed Coproducts. Journal of Capital Normal University, No. 3, 27-32.

Top