论文标题
强烈同型的轮毂适当的变形理论躺在双子和图复合物
Deformation theory of the wheeled properad of strongly homotopy Lie bialgebras and graph complexes
论文作者
论文摘要
众所周知，强烈同型lie lie bialgebras $ \ mathcal {h} olieb $的同型非平凡程度零推导的代数可以通过Grothendieck-Teichmuller lie algebra lie algebra $ \ mathfrak {grt} $识别。我们在本文中研究了轮式闭合$ \ MATHCAL {H} OLIEB^\ CRICTLEALROWLOWFEFT $（及其程度转移的版本$ \ Mathcal {h} olieb_ { Kontsevich Graph Complex的版本。这一结果使我们得出了一个令人惊讶的结论，即可以用\ textit {两}副本的直接总和将$ \ mathfrak {grt} $的直接总和以\ textit {两}的直接总和来确定同型非客气派生的谎言代数。作为一个说明性的例子，我们明确地描述了$ \ mathfrak中著名的四面体类是如何在两种同型不等式的方式中的$ \ mathcal {h} olieb^{\ mathcal {h} olieb^{\ mathcal {h} olieb^{\ mathcal {h} olieb^{
It is well-known that the Lie algebra of homotopy non-trivial degree zero derivations of the properad of strongly homotopy Lie bialgebras $\mathcal{H}olieb$ can be identified with the Grothendieck-Teichmuller Lie algebra $\mathfrak{grt}$. We study in this paper the derivation complex of the wheeled closure $\mathcal{H}olieb^\circlearrowleft$ (and of its degree shifted version $\mathcal{H}olieb_{p,q}^\circlearrowleft,\ \forall p,q\in\mathbb{Z}$) and establishing a quasi-isomorphism to a version of the Kontsevich graph complex. This result leads us to a surprising conclusion that the Lie algebra of homotopy non-trivial derivations of the wheeled properad $\mathcal{H}olieb^{\circlearrowleft}$ can be identified with the direct sum of \textit{two} copies of $\mathfrak{grt}$. As an illustrative example, we describe explicitly how the famous tetrahedron class in $\mathfrak{grt}$ acts as a derivation of $\mathcal{H}olieb^{\circlearrowleft}$ in two homotopy inequivalent ways.
