广义Poisson超代数的同调与上同调群

给出了广义Poisson超代数的同调和上同调群的基本性质.特别是,通过Hochschild上同调以及长正合列,建立了广义Poisson超代数上同调群的理论,刻画了这种代数的低阶上同调群.最后,决定了5-正合列以及它的泛中心扩张的核.     

Morphic cohomology and singular cohomology of motives over the complex numbers

Morphic cohomology and singular cohomology of motives over the complex numbers are defined via the triangulated category of motives. Regarding morphic cohomology as functors defined on the triangulated category of motives, natural transformations of morphic cohomology are studied.     

Twisted smooth Deligne cohomology

Deligne cohomology can be viewed as a differential refinement of integral cohomology, hence captures both topological and geometric information. On the other hand, it can be viewed as the simplest nontrivial version of a differential cohomology theory. While more involved differential cohomology theories have been explicitly twisted, the same has not been done to Deligne cohomology, although existence is known at a general abstract level. We work out what it means to twist Deligne cohomology, by taking degree one twists of both integral cohomology and de Rham cohomology. We present the main properties of the new theory and illustrate its use with examples and applications. Given how versatile Deligne cohomology has proven to be, we believe that this explicit and utilizable treatment of its twisted version will be useful.     

The mod 2 cohomology of the exceptional groups

In this note we prove the mod 2 cohomology of an exceptional Lie group can be computed from the rational cohomology. In fact the rational cohomology determines the mod 2 cohomology as an algebra over the Steenrod algebra.     

Non-Abelian Cohomology of Groups

Following Guin's approach to non-abelian cohomology [4] and, using the notion of a crossed bimodule, a second pointed set of cohomology is defined with coefficients in a crossed module, and Guin's six-term exact cohomology sequence is extended to a nine-term exact sequence of cohomology up to dimension 2     

Cohomology of partially ordered sets and local cohomology of section rings

We study local cohomology of rings of global sections of sheafs on the Alexandrov space of a partially ordered set. We give a criterion for a splitting of the local cohomology groups into summands determined by the cohomology of the poset and the local cohomology of the stalks. The face ring of a rational pointed fan can be considered as the ring of global sections of a flasque sheaf on the face poset of the fan. Thus we obtain a decomposition of the local cohomology of such face rings. Since the Stanley-Reisner ring of a simplicial complex is the face ring of a rational pointed fan, our main result can be interpreted as a generalization of Hochster's decomposition of local cohomology of Stanley-Reisner rings.     

The Hochschild cohomology of the quasi-entwining structure

We give a concept of quasi-entwining structure,and investigate the Hochschild cohomology of the quasi-entwining structure.We obtain the equivalent theorems on the Hochschild cohomology of the quasientwining structure.In particular,we get the isomorphism theorem between the Hochschild cohomology of coalgebra structures and the Hochschild cohomology of the dual algebra structures for the quasi-entwining structures of finite-dimensional algebras and coalgebras.     

Stable cohomology of compact homogeneous spaces

The cohomology of certain compact homogeneous spaces is studied. The notion of stable cohomology (invariant under the passage to a finite covering) is introduced; examples of the calculation of this cohomology (Theorem 1) and its application to the study of the structure of compact homogeneous spaces (Theorem 2) are given. Several conjectures about properties of stable cohomology related to various areas of mathematics (such as topology and the cohomology of discrete (in particular, polycyclic) groups) are stated.     

The Chen-Ruan cohomology of almost contact orbifolds

Comparing to the Ch-~Ruan cohomology theory for the almost complex orbifolds, we study the orbifold cohomology theory for almost contact orbifolds. We define the Chen-Ruan cohomology group of any almost contact orbifold. Using the methods for almost complex orbifolds, we define the obstruction bundle for any 3-multisector of the almost contact orbifolds and the Chen~Ruan cup product for the Che-Ruan cohomology. We also prove that under this cup product the direct sum of all dimensional orbifold cohomology groups constitutes a cohomological ring. Finally we calculate two examples.     

Hochschild cohomology of ring objects in monoidal categories

We define the Hochschild complex and cohomology of a ring object in a monoidal category enriched over abelian groups. We interpret the cohomology groups and prove that the cohomology ring is graded-commutative.     

Cohomology of fixed point sets and deformation of algebras

Under certain conditions the cohomology algebra (with appropriate coefficients) of the fixed point set of a G-space (G=Z/pZ=Zp, p prime or G=S¹) can be considered a deformation - in a purely algebraic sense - of the cohomology algebra of the space itself. On one hand this gives restrictions on the isomorphism type of algebras that can occur as cohomology algebra of the fixed point set of G-spaces if the cohomology algebra of the space itself is given. On the other hand it leads to the definition of obstructions for the cohomology algebra of the fixed point set to be isomorphic (as an ungraded algebra) to the cohomology algebra of the space itself.     

Z_n分次代数的Hochschild上同调群

本文给出了Z_n分次代数A的Hochschild上同调群的定义,对低阶Hochschild上同调群进行了刻画.利用第一阶Hochschild上同调群给出了Z_n分次代数为分次可分代数的充要条件,证明了第二阶Hochschild上同调群的零次分支与A的Hochschild扩张之间的一一对应关系.     

Cohomology theories based on Gorenstein injective modules

In this paper we study relative and Tate cohomology of modules of finite Gorenstein injective dimension. Using these cohomology theories, we present variations of Grothendieck local cohomology modules, namely Gorenstein and Tate local cohomology modules. By applying a sort of Avramov-Martsinkovsky exact sequence, we show that these two variations of local cohomology are tightly connected to the generalized local cohomology modules introduced by J. Herzog. We discuss some properties of these modules and give some results concerning their vanishing and non-vanishing.

     

Cohomology Algebras of Blocks of Finite Groups and Brauer Correspondence

M. Linckelmann defined the cohomology algebras of blocks of finite groups. This note is an attempt to analyze an inclusion of cohomology algebras of blocks that corresponds under Brauer correspondence through transfer maps between the Hochschild cohomology algebras of the blocks.Presented by Jon Carlson.     

Central extensions and deformations of Hom-Lie triple systems

In this paper, we study the cohomology theory of Hom-Lie triple systems generalizing the Yamaguti cohomology theory of Lie triple systems. We introduce the central extension theory for Hom-Lie triple systems and show that there is a one-to-one correspondence between equivalent classes of central extensions of Hom-Lie triple systems and the third cohomology group. We develop the 1-parameter formal deformation theory of Hom-Lie triple systems and prove that it is governed by the cohomology group.     

Vanishing of odd dimensional intersection cohomology II

For a variety where a connected linear algebraic group acts with only finitely many orbits, each of which admits an attractive slice, we show that the stratification by orbits is perfect for equivariant intersection cohomology with respect to any equivariant local system. This applies to provide a relationship between the vanishing of the odd dimensional intersection cohomology sheaves and of the odd dimensional global intersection cohomology groups. For example, we show that odd dimensional intersection cohomology sheaves and global intersection cohomology groups vanish for all complex spherical varieties. Received: 25 February 2000 / Accepted: 15 February 2001 / Published online: 23 July 2001     

Relative cohomology of finite groups and polynomial growth

This article investigates the cohomology of a finite group relative to a collection of sub-groups. In particular a new spectral sequence abutting to relative cohomology is given and is used to deduce that relative cohomology has polynomial growth.     

The homotopy category of pseudofunctors and translation cohomology

We develop the obstruction theory of the 2-category of abelian track categories, pseudofunctors and pseudonatural transformations by using the cohomology of categories. The obstructions are defined in Baues-Wirsching cohomology groups. We introduce translation cohomology to classify endomorphisms in the 2-category of abelian track categories. In a sequel to this paper we will show, under certain conditions which are satisfied by all homotopy categories, that a translation cohomology class determines the exact triangles of a triangulated category.     

Local cohomology based on a nonclosed support defined by a pair of ideals

We introduce a generalization of the notion of local cohomology module, which we call a local cohomology module with respect to a pair of ideals (I,J), and study its various properties. Some vanishing and nonvanishing theorems are given for this generalized version of local cohomology. We also discuss its connection with ordinary local cohomology.     

Low-dimensional cohomology of <Emphasis Type="Italic">q</Emphasis>-deformed Heisenberg-Virasoro algebra of Hom-type

Hom-Lie algebras were introduced by J. Hartwig, D. Larsson, and S. Silvestrov as a generalized Lie algebra. When studying the homology and cohomology theory of Hom-Lie algebras, the authors find that the low-dimensional cohomology theory of Hom-Lie algebras is not well studied because of the Hom-Jacobi identity. In this paper, the authors compute the first and second cohomology groups of the q-deformed Heisenberg-Virasoro algebra of Hom-type, which will be useful to build the low-dimensional cohomology theory of Hom-Lie algebras.