11 citations · 27 across the 15 of their papers we have counts for
16 papers
Deformations and homotopy theory of Rota-Baxter Lie algebras
Jun Chen, Kai Wang, Guodong Zhou
For Rota-Baxter Lie algebras, a homotopy cooperad is exhibited, whose cobar construction is shown to be the minimal model of the operad of Rota-Baxter Lie algebras by using algebra…
A Symmetric Counterexample to the Snashall--Solberg Conjecture
Kai Wang, Guodong Zhou
It is shown that the trivial extension of the Xu--Snashall algebra is a symmetric counterexample to the Snashall--Solberg conjecture, which states that the Hochschild cohomology ri…
Linearisation, splitting property and homotopy algebras
Seokbong Seol, Kai Wang
We study the linearisation of formal vector fields and homotopy algebras using graded coalgebras. We prove that a formal vector field is linearisable if and only if it satisfies a…
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…
BPS invariants from framed links
Kai Wang, Shengmao Zhu
In this article, we investigate the BPS invariants associated with framed links. We extend the relationship between the algebraic curve (i.e. dual -polynomial) and the BPS invar…
The bounded ideal monad on the category of quasi-metric spaces and its algebras
Kai Wang, Dexue Zhang
The notion of bounded ideals is introduced for quasi-metric spaces. Such ideals give rise to a monad, the bounded ideal monad, on the category of quasi-metric spaces and non-expans…
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…
Koszul duality, minimal model and -structure for differential algebras with weight
Jun Chen, Li Guo, Kai Wang +1
A differential algebra with weight is an abstraction of both the derivation (weight zero) and the forward and backward difference operators (weight ). In 2010 Loday establis…
Deformations and Cohomology Theory of Rota-Baxter Systems
Yuming Liu, Kai Wang, Liwen Yin
Inspired by the work of Wang and Zhou [4] for Rota-Baxter algebras, we develop a cohomology theory of Rota-Baxter systems and justify it by interpreting the lower degree cohomology…
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…
The minimal model of Rota-Baxter operad with arbitrary weight
Kai Wang, Guodong Zhou
This paper investigates Rota-Baxter associative algebras of of arbitrary weights, that is, associative algebras endowed with Rota-Baxter operators of arbitrary weights from an oper…
Deformations and homotopy theory of Rota-Baxter algebras of any weight
Kai Wang, Guodong Zhou
This paper studies formal deformations and homotopy theory of Rota-Baxter algebras of any weight. We define an -algebra, which controls simultaneous deformations of assoc…
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…
Cohomology theory of averaging algebras, -structures and homotopy averaging algebras
Kai Wang, Guodong Zhou
This paper studies averaging algebras, say, associative algebras endowed with averaging operators. We develop a cohomology theory for averaging algebras and justify it by interpret…