论文标题
兼容，分裂和家庭Loday-Elgebras
Compatible, split and family Loday-algebras
论文作者
论文摘要
给定一个非对称operad $ \ mathcal {o} $，我们首先构造了两个新的非对称operads $ \ Mathcal {o}^{\ Mathrm {Comp}} $和$ \ Mathcal {o}这些作业分别可用于研究兼容和分裂的洛达伊代数。作为Operad $ \ Mathcal {O}^{\ Mathrm {Comp}} $的应用，我们表明兼容的关联代数的共同体具有Gerstenhaber结构。我们将Operad $ \ Mathcal {O}^\ Mathrm {dend} $的应用程序应用于Dendriform代数，并找到对其他Loday-Algebras的概括。最后，我们构造了另一个Operad $ \ Mathrm {Fam}（\ Mathcal {O}^ω）^\ Mathrm {dend} $，以研究文献中最近引入的Dendriform-family-family代数。我们还定义和研究同型树突形家庭代数。
Given a nonsymmetric operad $\mathcal{O}$, we first construct two new nonsymmetric operads $\mathcal{O}^{\mathrm{comp}}$ and $\mathcal{O}^{\mathrm{Dend}}$. These operads are respectively useful to study compatible and split Loday-algebras. As an application of the operad $\mathcal{O}^{\mathrm{comp}}$, we show that the cohomology of a compatible associative algebra carries a Gerstenhaber structure. We give an application of the operad $\mathcal{O}^\mathrm{Dend}$ to dendriform algebras and find generalizations to other Loday-algebras. In the end, we construct another operad $\mathrm{Fam}(\mathcal{O}^Ω)^\mathrm{Dend}$ to study dendriform-family algebras recently introduced in the literature. We also define and study homotopy dendriform-family algebras.
