p-Power Points and Modules of Constant p-Power Jordan Type

We study finitely generated modules over k[G] for a finite abelian p-group G, char(k) = p, through restrictions to certain subalgebras of k[G]. We define p-power points, shifted cyclic p-power order subgroups of k[G], and give characterizations of these. We define modules of constant p ^t -Jordan type, constant p ^t -power-Jordan type as generalizations of modules of constant Jordan type, and p ^t -support, nonmaximal p ^t -support spaces. We obtain a filtration of modules of constant Jordan type with modules of constant p-power Jordan type as the last term and give examples of non-isomorphic modules of constant p-power Jordan type having the same constant Jordan type.     

Modules of Constant Jordan Type with Small Non-Projective Part

Let E be an elementary abelian p-group of rank r and let k be an algebraically closed field of characteristic p. We prove that if M is a kE-module of stable constant Jordan type [a ₁]...[a _t ] with ∑? _j a _j ?≤?min(r???1, p???2) then a ₁?=?...?=?a _t ?=?1. The proof uses the theory of Chern classes of vector bundles on projective space.     

Modules of Constant Jordan Type with One Non-Projective Block

Let k be an algebraically closed field of characteristic p and G be a finite group of p-rank at least two. We prove that there cannot exist a finite dimensional kG-module of stable constant Jordan type [a] with 2 ≤ a ≤ p − 2. This is a generalisation of a conjecture of Carlson, Friedlander and Pevtsova.     

Simple Modules for the Restricted Cartan Type Lie Algebras

The simple modules with homogeneous characters are considered, their dimension formulas are determined.Presented by D. Passman.     

Approximation Presentations of Modules and Homological Conjectures

In this article we give a sufficient condition of the existence of 𝕎 ^t -approximation presentations. We also introduce property (W ^k ). As an application of the existence of 𝕎 ^t -approximation presentations we give a connection between the finitistic dimension conjecture, the Auslander–Reiten conjecture, and property (W ^k ).     

Jordan Modules and Jordan Ideals of Reflexive Algebras

Let ${\mathcal{L}}$ be a completely distributive subspace lattice on a Banach space and alg ${\mathcal{L}}$ the associated reflexive algebra. Suppose that the following $$\mbox{Condition A:}\dim(F/F\wedge F_-)\ne1\;\; \mbox{for all}\;\;F\in\mathcal{L}$$ holds; note that if ${\mathcal{L}}$ is an atomic Boolean subspace lattice, this condition means that every atom of ${\mathcal{L}}$ has dimension at least two. It is shown that every reflexive Jordan Alg ${\mathcal{L}}$ -module is an associative Alg ${\mathcal{L}}$ -module. We give an example which shows that if the Condition A is removed, then the conclusion is not necessarily true. Moreover, we prove that all reflexive Jordan ideals of Alg ${\mathcal{L}}$ are associative ideals in the case that no the Condition A is assumed. The same conclusions hold for weakly closed Jordan modules and weakly closed Jordan ideals if the rank one subalgebra of Alg ${\mathcal{L}}$ is weakly dense in Alg ${\mathcal{L}}$ .     

限制李超代数的诱导模

In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.     

有常秩的投射模

本文定义更具一般性的模(未必是有限生成投射模)的常秩的概念,并证明了如果M有常秩n,∧~n M是有限生成的,则M是有限生成的,还证明了若M是有常秩n的投射模,则M一定是有限生成的。     

A Category of Restricted Modules for the Ovisenko-Roger Algebra

In this paper, we study a category of restricted modules for the Ovsienko-Roger algebra, which is an extension of the Virasoro algebra of its tensor density module of degree one. We construct and characterize simple modules in this category and give natural free field realizations of certain restricted modules using the Weyl vertex algebra.

     

Character Formulas for a Class of Simple Restricted Modules over the Simple Lie Superalgebras of Witt Type

Let F be an algebraically closed field of prime characteristic, and W(m, n, 1) be the simple restricted Lie superalgebra of Witt type over F, which is the Lie superalgebra of superderivations of the superalgebra ■(m; 1) ■∧(n), where ■(m; 1) is the truncated polynomial algebra with m indeterminants and ∧(n) is the Grassmann algebra with n indeterminants. In this paper, the author determines the character formulas for a class of simple restricted modules of W(m, n, 1) with atypical weights of type...     

Quantum Incompressibility and Razumov Stroganov Type Conjectures

We establish a correspondence between polynomial representations of the Temperley and Lieb algebra and certain deformations of the Quantum Hall Effect wave functions. When the deformation parameter is a third root of unity, the representation degenerates and the wave functions coincide with the domain wall boundary condition partition function appearing in the conjecture of A.V. Razumov and Y.G. Stroganov. In particular, this gives a proof of the identification of the sum of the entries of the O(n) transfer matrix and a six vertex-model partition function, alternative to that of P. Di Francesco and P. Zinn-Justin. submitted 22/04/05, accepted 23/08/05     

On Projective Modules with Constant Ranks

On Projective Modules with Constant RanksIn this paper,we investigate module structures of rings over which every finitely generated projective module with constant rank is stably free. As applications,we give characterizations of some related rings.     

Banach空间上套代数的弱闭Jordan模

设■为Banach空间X上的套,D为Alg■的弱闭Jordan模.若对任意N∈■,dim(N/■_)≠1与N拓扑可补至少有一个成立,则■必为Alg■的模.     

Semisimple Modules for Finite Groups of Lie Type

Let k be an algebraically closed field of characteristic p >0, and let G be a connected, reductive algebraic group overk. In [8] and [11], conditions on the dimension of rationalG modules were seen to imply semisimplicity of these modules.In [8], certain of these conditions were extended to cover thefinite groups of Lie type. In this paper, we extend some ofthe results of [11] to cover these finite Lie type groups. Themain such extension is the following result.     

具有三角分解李代数的广义限制单模

通过广义限制李代数的定义,得到了所有具有三角分解的李代数的广义限制单模,并且作为一个例子,计算了李代数V3G的所有广义限制单模以及它们的维数.     

Structure of T Modules and Restricted Duals: The Classical and the Quantum Case

Abstract

A concrete realization of Enright's T modules is obtained. This is used to show their self-duality. As a consequence, the restricted duals of Verma modules are also identified.     

限制Hamiltonian型及Contact型李代数的不可约表示

设L=H（2r;1）或K（2r+1;1）是定义在特征p>2的代数封闭域F上的限制Hamiltonian型或Contact型李代数.在对广义Jacobson-Witt代数及特殊代数不可约表示的研究基础上,通过定义L的如下阶化:L=L_[q],I,其中I是{1,2,…,r}的子集,得到当p-特征函数χ是正则半单时,所有不可约U_χ（L）-模都是从不可约U_χ(L_[O].I)-模诱导的.