论文标题
Rota-Baxter代数，树突状代数和井的基本序列的统一扩展理论
A unified extension theory of Rota-Baxter algebras, dendriform algebras, and a fundamental sequence of Wells
论文作者
论文摘要
rota-baxter代数$ a_r $是配备了杰出的rota-baxter操作员$ r $的代数$ a $。 Rota-baxter代数与Loday引入的树突状代数密切相关。在本文中，我们首先考虑Rota-baxter代数的非亚伯扩展理论，并通过引入非亚伯式的共同体来对其进行分类。接下来，给定一个非阿布尔延长$ 0 \ rightarrow b_s \ rightArrow e_u \ rightarrow a_r a_r \ righatrow \ rightarrow 0 $ rota-baxter代数，我们构建了井类型精确序列，并在扩展rota-baxter automormormormormormormormormormormormormormorphist $β\ in \ intrm rm rmm {aut aut aut aut aut}（$ s）（b_s）$ {$}（b_s）（b_s）（ $α\ in \ mathrm {aut}（a_r）$ to $ \ mathrm {aut}（e_u）$中的自动形态。我们通过考虑针对树突状代数的类似研究来结束本文。
A Rota-Baxter algebra $A_R$ is an algebra $A$ equipped with a distinguished Rota-Baxter operator $R$ on it. Rota-Baxter algebras are closely related to dendriform algebras introduced by Loday. In this paper, we first consider the non-abelian extension theory of Rota-Baxter algebras and classify them by introducing the non-abelian cohomology. Next, given a non-abelian extension $0 \rightarrow B_S \rightarrow E_U \rightarrow A_R \rightarrow 0$ of Rota-Baxter algebras, we construct the Wells type exact sequences and find their role in extending a Rota-Baxter automorphism $β\in \mathrm{Aut}(B_S)$ and lifting a Rota-Baxter automorphism $α\in \mathrm{Aut}(A_R)$ to an automorphism in $\mathrm{Aut}(E_U)$. We end this paper by considering a similar study for dendriform algebras.
