On derivation deviations in an abstract pre-operad

导出导子控制dg（预）operad上dg代数的反导出形变

Derived derivations govern contraderived deformations of dg algebras over dg (pr)operads

本研究证明dg（预）operad上dg代数的导出导子DGLA的Hinich单纯神经，等价于Positselski反导出dg范畴中该代数的形变空间，解决了Hinich关于导出形变一般存在性的反例问题，并推广了其同调下有界时的相关结果。

模 operads、迭代分配律和电路代数的神经定理

Modular operads, iterated distributive laws and a nerve theorem for circuit algebras

本文通过扩展模 operads 的结果，构建了电路代数的图示计算和单子，并证明了抽象神经定理，揭示了有向电路代数与轮化 props 的等价关系。

M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra

We show that the zeroth cohomology of M. Kontsevich's graph complex is isomorphic to the Grothendieck-Teichmueller Lie algebra grt_1. The map is explicitly described. This result has applications to deformation quantization and Duflo theory. We also compute the homotopy derivations of the Gerstenhaber operad. They are parameterized by grt_1, up to one class (or two, depending on the definitions). More generally, the homotopy derivations of the (non-unital) E_n operads may be expressed through the cohomology of a suitable graph complex. Our methods also give a second proof of a result of H. Fur…

超树与$\boldsymbol{\rm FMan}$ 操作子的嵌入

Hypertrees and embedding of the $\mathrm{FMan}$ operad

该研究围绕Dotsenko关于FMan操作子可嵌入ComPreLie操作子的猜想展开，通过建立Greg树与PreLie操作子扭的联系、给出ComPreLie的有根超树森林组合描述等，借助操作子扭技术证明了该猜想。

Tetracomposition

We consider basic algebraic constructions associated with an abstract pre-operad, such as a $\smile$-algebra, total composition $\bul$, pre-coboundary operator $\de$, tribraces $\{\cdot,\cdot,\cdot\}$ and tetrabraces $\{\cdot,\cdot,\cdot,\cdot\}$. A derivation deviation of the pre-coboundary operator over the tetrabraces is calculated in terms of the $\smile$-multiplication and tribraces.

循环代数的抽象Hodge分解与极小模型

Abstract Hodge decomposition and minimal models for cyclic algebras

本文证明配备Hodge分解的循环operad代数存在由树求和构造的极小模型，且该模型在同伦意义下唯一。