论文标题
Rota-baxter Leibniz代数的统一，变形和扩展
Cohomology, deformations and extensions of Rota-Baxter Leibniz algebras
论文作者
论文摘要
Rota-baxter Leibniz代数是Leibniz代数$（\ Mathfrak {g}，[〜，〜] _ {\ Mathfrak {g}}）$，配备了Rota-Baxter操作员$ t：\ Mathfrak {g} \ rightarrow \ rightarrow \ Mathfrak} $。我们定义了Rota-Baxter Leibniz代数的表示和双重表示。接下来，我们定义了Rota-baxter Leibniz代数的共同体学理论。我们还研究了Rota-baxter Leibniz代数的无限和形式变形理论，并表明我们的共同体是变形的共同体学。此外，我们定义了Rota-Baxter Leibniz代数的Abelian扩展，并表明此类扩展的等效类别与共同体学组有关。
A Rota-Baxter Leibniz algebra is a Leibniz algebra $(\mathfrak{g},[~,~]_{\mathfrak{g}})$ equipped with a Rota-Baxter operator $T : \mathfrak{g} \rightarrow \mathfrak{g}$. We define representation and dual representation of Rota-Baxter Leibniz algebras. Next, we define a cohomology theory of Rota-Baxter Leibniz algebras. We also study the infinitesimal and formal deformation theory of Rota-Baxter Leibniz algebras and show that our cohomology is deformation cohomology. Moreover, We define an abelian extension of Rota-Baxter Leibniz algebras and show that equivalence classes of such extensions are related to the cohomology groups.
