6 citations · 11 across the 8 of their papers we have counts for
10 papers
Disuccessors, Gröbner-Shirshov bases and free L-dendriform algebras
Huhu Zhang, Xing Gao, Yuanyuan Zhang
In this paper, we prove respectively that the disuccessor operations on the associative operad $\as$, the Lie operad $\lie$, and the pre-Lie operad $\prelie$ preserve Gröbner-Shirs…
Free weighted differential (-tri)dendriform algebras
Yuanyuan Zhang, Huhu Zhang, Tingzeng Wu +1
In the present paper, we propose the concepts of weighted differential (-tri)dendriform algebras and give some basic properties of them. The corresponding free objects are const…
Deformations and cohomology theory of -family Rota-Baxter algebras of arbitrary weight
Chao Song, Kai Wang, Yuanyuan Zhang
In this paper, we firstly construct an -algebra via the method of higher derived brackets, whose Maurer-Cartan elements correspond to relative -family Rota-Baxter a…
Rota-Baxter family -associative conformal algebras and their cohomology theory
Yuanyuan Zhang, Jun Zhao, Genqiang Liu
In this paper, we first propose the concept of Rota-Baxter family -associative conformal algebras, then we study the cohomology theory of Rota-Baxter family -associative conf…
Free -Rota-Baxter systems and Gröbner-Shirshov bases
Yuanyuan Zhang, Huhu Zhang, Xing Gao
In this paper, we propose the concept of an -Rota-Baxter system, which is a generalization of a Rota-Baxter system and an -Rota-Baxter algebra of weight zero. In the framewor…
A Whittaker category for the Symplectic Lie algebra
Yang Li, Jun Zhao, Yuanyuan Zhang +1
For any , let be the subalgebra of spanned by all long negative root vectors , . An $\mathfr…
Families of algebraic structures
Loic Foissy, Dominique Manchon, Yuanyuan Zhang
We give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the se…
Free pre-Lie family algebras
Dominique Manchon, Yuanyuan Zhang
In this paper, we first define the pre-Lie family algebra associated to a dendriform family algebra in the case of a commutative semigroup. Then we construct a pre-Lie family algeb…
Free Rota-Baxter family algebras and Free (tri)dendriform family algebras
Yuanyuan Zhang, Xing Gao, Dominique Manchon
In this paper, we first construct the free Rota-Baxter family algebra generated by some set in terms of typed angularly -decorated planar rooted trees. As an application, we…
Free (tri)dendriform family algebras
Yuanyuan Zhang, Xing Gao, Dominique Manchon
In this paper, we first prove that a Rota-Baxter family algebra indexed by a semigroup induces an ordinary Rota-Baxter algebra structure on the tensor product with the semigroup al…