6 papers
Quasi-triangular Jordan D-bialgebras and extended relative Rota-Baxter operators
Dilei Lu, Dongping Hou, Yuanchang Lin
This paper introduces quasi-triangular Jordan D-bialgebras, which are constructed from solutions of the Jordan Yang-Baxter equation (JYBE) with invariant symmetric parts. We first…
Post-Poisson algebras, extended -operators and extended Poisson Yang-Baxter equations
Yuanchang Lin, Dilei Lu
This paper introduces the extended -operators on Poisson algebras as a natural generalization of ordinary -operators, together with the extended Poisson Y…
Skew-symmetric Frobenius dialgebras, diassociative bialgebras and Yang-Baxter equations
Dilei Lu
A diassociative algebra (or dialgebra), a generalization of associative algebras with two associative products, is a fundamental algebraic structure of great importance and wide-ra…
Properties, deformation quantizations and bialgebras for dual pre-Poisson algebras
Dilei Lu
A dual pre-Poisson algebra is an algebraic structure that integrates a permutative algebra and a Leibniz algebra under certain compatibility conditions. As the Koszul dual notion o…
Quasi-triangular and factorizable Poisson bialgebras
Yuanchang Lin, Dilei Lu
In this paper, we introduce the notions of quasi-triangular and factorizable Poisson bialgebras. A factorizable Poisson bialgebra induces a factorization of the underlying Poisson…
A bialgebra theory of post-Lie algebras via Manin triples and generalized Hessian Lie groups
Dilei Lu, Chengming Bai, Li Guo
We develop a bialgebra theory of post-Lie algebras that can be characterized by Manin triples of post-Lie algebras associated to a bilinear form satisfying certain invariant condit…