11 citations · 20 across the 9 of their papers we have counts for
10 papers
Modified Rota-Baxter operators of non-zero weight on -Lie algebras
Shuangjian Guo, Yufei Qin, Guodong Zhou
In this paper, we introduce the notion of modified Rota-Baxter operators of non-zero weight on -Lie algebras and provide some examples. Next, we give various constructions of mo…
L-algebras and their ideals: from simplicity to semidirect products
Silvia Properzi, Yufei Qin
In this paper, we investigate the ideals of semidirect products of L-algebras and the structure of simple L-algebras. We provide a precise characterization of the ideals of semidir…
From homotopy Rota-Baxter algebras to Pre-Calabi-Yau and homotopy double Poisson algebras
Yufei Qin, Kai Wang
In this paper, we investigate pre-Calabi-Yau algebras and homotopy double Poisson algebras arising from homotopy Rota-Baxter structures. We introduce the notion of cyclic homotopy…
Deformation theory and Koszul duality for Rota-Baxter systems
Yufei Qin, Kai Wang, Guodong Zhou
This paper investigates Rota-Baxter systems in the sense of Brzeziński from the perspective of operad theory. The minimal model of the Rota-Baxter system operad is constructed, equ…
Gröbner-Shirshov bases and linear bases for free multi-operated algebras over algebras with applications to differential Rota-Baxter algebras and integro-differential algebras
Zuan Liu, Zihao Qi, Yufei Qin +1
Quite much recent studies has been attracted to the operated algebra since it unifies various notions such as the differential algebra and the Rota-Baxter algebra. An -operated…
-structures and cohomology theory of compatible -operators and compatible dendriform algebras
Apurba Das, Shuangjian Guo, Yufei Qin
The notion of -operator is a generalization of the Rota-Baxter operator in the presence of a bimodule over an associative algebra. A compatible -operator…
Cohomology theory of Rota-Baxter pre-Lie algebras of arbitrary weights
Shuangjian Guo, Yufei Qin, Kai Wang +1
This paper is devoted to studying deformation, cohomology theory of Rota-Baxter pre-Lie algebras of arbitrary weights. First we give the notion of a new representation of a Rota-Ba…
Deformations and cohomology theory of Rota-Baxter -Lie algebras of arbitrary weights
Shuangjian Guo, Yufei Qin, Kai Wang +1
A cohomology theory of weighted Rota-Baxter -Lie algebras is introduced. Formal deformations, abelian extensions, skeletal weighted Rota-Baxter -Lie 2-algebras and crossed mo…
Gröbner-Shirshov bases and linear bases for free differential type algebras over algebras
Zihao Qi, Yufei Qin, Guodong Zhou
We study a question which can be roughly stated as follows: Given a (unital or nonunital) algebra together with a Gröbner-Shirshov basis , consider the free operated algebra…
Free objects and Gröbner-Shirshov bases in operated contexts
Zihao Qi, Yufei Qin, Kai Wang +1
This paper investigates algebraic objects equipped with an operator, such as operated monoids, operated algebras etc. Various free object functors in these operated contexts are ex…