单Leibniz代数上双模范畴中的Ext群

On Leibniz cohomology

In this paper we prove the Leibniz analogue of Whitehead's vanishing theorem for the Chevalley-Eilenberg cohomology of Lie algebras. As a consequence, we obtain the second Whitehead lemma for Leibniz algebras. Moreover, we compute the cohomology of several Leibniz algebras with adjoint or irreducible coefficients. Our main tool is a Leibniz analogue of the Hochschild-Serre spectral sequence, which is an extension of (the dual of) a spectral sequence of Pirashvili for Leibniz homology from symmetric bimodules to arbitrary bimodules.

Homological splitting results for modules over Leibniz algebras

A unified splitting result for Ext calculated in the category of modules over a Leibniz algebra is given for the case where coefficients are either both symmetric modules or both antisymmetric modules. This is a generalization of results of Loday and Pirashvili and others.

正合范畴上双模的一个Dundas-McCarthy定理

A Dundas-McCarthy theorem for bimodules over exact categories

从正合范畴$C$上的双模$M$，我们定义了一个正合范畴$C\ltimes M$，其投影下到$C$。这种构造对正合范畴的某些分裂平方零扩张进行了分类。我们表明，迹映射诱导的相对$K$ -理论的$C\ltimes M$和它的相对拓扑循环同调之间的等价性。当应用于环$A$上的双生成投射模范畴上的双模$\hom(-,-\otimes_AM)$时，恢复了环的分裂平方零扩张的经典Dundas-McCarthy定理.

Projective and Reedy model category structures for (infinitesimal) bimodules over an operad

We construct and study projective and Reedy model category structures for bimodules and infinitesimal bimodules over topological operads. Both model structures produce the same homotopy categories. For the model categories in question, we build explicit cofibrant and fibrant replacements. We show that these categories are right proper and under some conditions left proper. We also study the extension/restriction adjunctions.

Leibniz代数的形变量子化

Deformation quantization of Leibniz algebras

本文分为两部分.第一部分是对莱布尼茨代数在李架上的积分方法的回顾和推广，包括了一种新的积分2-余圈的方法（见引理3.9）。在第二部分中，我们利用一个莱布尼兹代数h的局部积分，利用一个Baker-Campbell-Hausdorff型公式，对它的线性对偶h^* 进行形变量子化。更准确地说，我们定义了指数函数集上的自然齿条积，它扩展到C^{ \infty }（h^*）上的齿条作用。

Soergel Bimodules, the Steenrod Algebra and Triply Graded Link homology

Soergel bimodules and their Hochschild homology are known to be important in the context of link homology. In this article we observe that Soergel bimodules may be naturally identified as the cohomology of well-defined objects in the category of spectra. This allows us to define forms of Soergel bimodules over the integers after inverting 2, indexed by elements in Braid groups associated to compact Lie groups of adjoint type. Reducing the Soergel bimodules modulo an odd prime, we endow the bimodules with an action of the reduced Steenrod algebra. This action extends to an action of the reduced…