4 papers · 1 filter
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…