Complexity and cohomology of cohomological Mackey functors

Let k be a field of characteristic p>0. Call a finite group G a poco group over k if any finitely generated cohomological Mackey functor for G over k has polynomial growth. The main result of this paper is that G is a poco group over k if and only if the Sylow p-subgroups of G are cyclic, when p>2, or have sectional rank at most 2, when p=2.A major step in the proof is the case where G is an elementary abelian p-group. In particular, when p=2, all the extension groups between simple functors can be determined completely, using a presentation of the graded algebra of self extensions of the simple functor , by explicit generators and relations.     

Cyclic cohomology of Banach algebras of quivers and their inverse semigroups

In this paper, we consider the path semigroup ?¹${?}^1$-algebra for a quiver and the inverse semigroup ?¹${?}^1$-algebra of a quiver, the latter of which can be used in the construction of Cuntz–Krieger algebras. The main objectives of the paper are to determine the simplicial and cyclic cohomology groups of these algebras. First, we determine the simplicial and cyclic cohomology of the path algebra of the quiver, showing the simplicial cohomology groups of dimension n   vanish for n>1$n>1$. We then determine the simplicial and cyclic cohomology of the inverse semigroup algebra. The work uses the Connes–Tzygan long exact sequence.     

Tate cohomology and periodic localization of polynomial functors

In this paper, we show that Goodwillie calculus, as applied to functors from stable homotopy to itself, interacts in striking ways with chromatic aspects of the stable category. Localized at a fixed prime p, let T(n) be the telescope of a v_n self map of a finite S–module of type n. The Periodicity Theorem of Hopkins and Smith implies that the Bousfield localization functor associated to T(n)_* is independent of choices. Goodwillies general theory says that to any homotopy functor F from S–modules to S–modules, there is an associated tower under F, {P_dF}, such that FP_dF is the universal arrow to a d–excisive functor. Our first main theorem says that P_dFP_d-1F always admits a homotopy section after localization with respect to T(n)_* (and so also after localization with respect to Morava K–theory K(n)_*). Thus, after periodic localization, polynomial functors split as the product of their homogeneous factors. This theorem follows from our second main theorem which is equivalent to the following: for any finite group G, the Tate spectrum is weakly contractible. This strengthens and extends previous theorems of Greenlees–Sadofsky, Hovey–Sadofsky, and Mahowald–Shick. The Periodicity Theorem is used in an essential way in our proof. The connection between the two theorems is via a reformulation of a result of McCarthy on dual calculus. Mathematics Subject Classification (2000) 55P65, 55N22, 55P60, 55P91     

Metrizability of Clifford topological semigroups

We prove that a countably compact Clifford topological semigroup S is metrizable if and only if the set E={e∈S:ee=e} of idempotents of S is a metrizable G _δ -set in S.     

Local cohomology,cofiniteness and homological functors of modules

Czechoslovak Mathematical Journal - Let I be an ideal of a commutative Noetherian ring R. It is shown that the R-modules H (M) are I-cofinite for all finitely generated R-modules M and all j...     

A generalized Clifford theorem of semigroups

A U-abundant semigroup S in which every H-class of S contains an element in the set of projections U of S is said to be a U-superabundant semigroup.This is an analogue of regular semigroups which are unions of groups and an analogue of abundant semigroups which are superabundant.In 1941,Clifford proved that a semigroup is a union of groups if and only if it is a semilattice of completely simple semigroups.Several years later,Fountain generalized this result to the class of superabundant semigroups.In this p...     

Clifford拟正则半群的半直积

给出了两个半群S和T的半直积是Clifford拟正则半群的充要条件，同时还讨论了S和T^e半直积的结构，其中T^e＝{t^e|Vt∈T,Vc∈E（S）}。     

E-自反逆半群上的Clifford同余

研究E-自反逆半群上的Clifford同余.本文中的结果是James[1],McAlister[2],Petrich[3]和Reilly[4]等人关于E-酉逆半群上的相应同余定理在E-自反逆半群上的自然推广.     

具有Clifford断面的正则纯正半群

给出了具有Clifford断面的右正规纯正半群的等价刻画,得到了具有Clifford断面的正则纯正半群的次直积分解,证明了具有Clifford断面的正则纯正半群一定是正则纯正群．     

左Clifford拟正则半群的半直积和圈积

在半群不含单位元的情况下,给出了两个半群的半直积和圈积是左Clifford拟正则半群的充分必要条件.     

Various notions of weak injectivity over Clifford semigroups

We study various notions of weak injectivity of acts over a Clifford semigroup. In addition we characterize weak self-injectivities of several classes of Clifford semigroups constructed via particular kinds of groups and group homomorphisms. Research of X. Zhang supported by the China Scholarship Council No. 2006101056. Research of Y. Wang supported by National Natural Science Foundation of China Research Grant 10571181.     

The attainability and solvability spectra of varieties of Clifford semigroups

Omsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 5, pp. 59–67, September–October, 1991.     

On the finiteness properties of extension and torsion functors of local cohomology modules

Let be a commutative Noetherian ring with non-zero identity, and ideals of with , and a finitely generated -module. In this paper, for fixed integers and , we study the finiteness of and in several cases.

     

Characterizing compact Clifford semigroups that embed into convolution and functor-semigroups

We study algebraic and topological properties of the convolution semigroup of probability measures on a topological groups and show that a compact Clifford topological semigroup S embeds into the convolution semigroup P(G) over some topological group G if and only if S embeds into the semigroup exp(G)\exp(G) of compact subsets of G if and only if S is an inverse semigroup and has zero-dimensional maximal semilattice. We also show that such a Clifford semigroup S embeds into the functor-semigroup F(G) over a suitable compact topological group G for each weakly normal monadic functor F in the category of compacta such that F(G) contains a G-invariant element (which is an analogue of the Haar measure on G).