Abstract
In this paper, the Heisenberg doubles and Long dimodules of a BiHom-Hopf algebra are introduced. Then, we discussed the relation between BiHom-Hopf equation and BiHom-pentagon equation, and we obtain the solutions of BiHom-Hopf equation from Heisenberg doubles. We also showed that the parametric generalized Long dimodules can provide the solutions of BiHom-Yang-Baxter equation and generalized D-equation.
Funder
China Postdoctoral Science Foundation
National Natural Science Foundation of China
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference23 articles.
1. Deformation of Lie algebras using σ-derivations;J. Algebra,2006
2. q-Witt algebras, q-Lie algebras, q-holomorph structure and representations;Algebra Colloq.,1999
3. Yetter-Drinfeld modules for Hom-bialgebras;J. Math. Phys.,2014
4. Hom-algebras structures;J. Gen. Lie Theory Appl.,2008
5. Makhlouf, A., and Silvestrov, S. (2008). Generalized Lie theory in Mathematics, Physics and Beyond, Springer. Chapter 17.