arXiv subjects

Xueru Wu

Publications and source records attributed to Xueru Wu.

3 recordsLinked to original sources

arXiv2022

Deformations of relative Rota-Baxter operators on Leibniz Triple Systems

In this paper, we introduce the cohomology theory of relative Rota-Baxter operators on Leibniz triple systems. We use the cohomological approach to study linear and formal deformations of relative Rota-Baxter operators. In particular, formal deformations and extendibility of order $n$ deformations of a relative Rota-Baxter operators are also characterized in terms of the cohomology theory. We also consider the relationship between cohomology of relative Rota-Baxter operators on Leibniz algebras and associated Leibniz triple systems.

math.RA↗

arXiv2022

Relative Rota-Baxter operators of nonzero weights on Lie Triple Systems

In this paper, we introduce the notion of a relative Rota-Baxter operator of weight $λ$ on a Lie triple system with respect to an action on another Lie triple system, which can be characterized by the graph of their semidirect product. We also establish a cohomology theory for a relative Rota-Baxter operator of weight $λ$ on Lie triple systems and use the first cohomology group to classify infinitesimal deformations.

math.RA↗

arXiv2021

Cohomology of Leibniz Triple Systems and its applications

In this paper, we introduce the first and third cohomology groups on Leibniz triple systems, which can be applied to extension theory and $1$-parameter formal deformation theory. Specifically, we investigate the central extension theory for Leibniz triple systems and show that there is a one-to-one correspondence between equivalent classes of central extensions of Leibniz triple systems and the third cohomology group. We study the $T^*$-extension of a Leibniz triple system and we determined that every even-dimensional quadratic Leibniz triple system $(\mathfrak{L},B)$ is isomorphic to a $T^*$-extension of a Leibniz triple system under a suitable condition. We also give a necessary and sufficient condition for a quadratic Leibniz triple system to admit a symplectic form. At last, we develop the $1$-parameter formal deformation theory of Leibniz triple systems and prove that it is governed by the cohomology groups.

math.RA↗