The p-Rank of the Incidence Matrix of Intersecting Linear Subspaces

Let V be a vector space of dimension n+1 over a field of p ^t elements. A d-dimensional subspace and an e-dimensional subspace are considered to be incident if their intersection is not the zero subspace. The rank of these incidence matrices, modulo p, are computed for all n, d, e and t. This result generalizes the well-known formula of Hamada for the incidence matrices between points and subspaces of given dimensions in a finite projective space. A generating function for these ranks as t varies, keeping n, d and e fixed, is also given. In the special case where the dimensions are complementary, i.e., d+e=n+ 1, our formula improves previous upper bounds on the size of partial m-systems (as defined by Shult and Thas).     

具有性质(G'_k)的Wakamatsu倾斜模

本文引进了具有性质(G'k)的Wakamatsu倾斜模的概念,并用同调有限子范畴的性质对其进行了刻画．     

Structure of cohomology modules of linear bundles overG/B

We study the cohomologyG-modules of linear bundles over flag spacesG/B for algebraically closed fields of prime characteristic. Some series of submodules and quotient modules of these modules are described. Translated by S. K. Lando Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 10–17, July, 1997.     

挠自由模的秩

本文讨论了无单位元环上挠自由模的极大无关子集,证明了左 ore 整环上挠自由模的极大无关子集都有相同的势,推广了文献的许多结果.     

Multivariable moment problems

In this paper we solve moment problems for Poisson transforms and, more generally, for completely positive linear maps on unital C^*-algebras generated by universal row contractions associated with , the free semigroup with n generators. This class of C*-algebras includes the Cuntz-Toeplitz algebra (resp. ) generated by the creation operators on the full (resp. symmetric, or anti-symmetric)) Fock space with n generators. As consequences, we obtain characterizations for the orbits of contractive Hilbert modules over complex free semigroup algebras such as ,and, more generally, the quotient algebra , where J is an arbitrary two-sided ideal of . All these results are extended to the generalized Cuntz algebra , where G_i⁺ are the positive cones ofdiscrete subgroups G_i⁺ of the real line . Moreover, we characterize the orbits of Hilbert modules over the quotient algebra , where J is an arbitrary two-sided ideal ofthe free semigroup algebra .     

Fock Space Realizations of Imaginary Verma Modules

This work expands to the setting of the results of H. Jakobsen and V. Kac and independently D. Bernard and G. Felder on the realization of , in terms of infinite sums of partial differential operators. We note in the paper that, in the generic case, these geometric constructions are just realizations of the imaginary Verma modules studied by V. Futorny. Presented by A. VerschorenMathematics Subject Classifications (2000) Primary: 17B67, 81R10.     

Gorenstein Flat Covers and Gorenstein Cotorsion Modules Over Integral Group Rings

Every module over an Iwanaga–Gorenstein ring has a Gorenstein flat cover [13] (however, only a few nontrivial examples are known). Integral group rings over polycyclic-by-finite groups are Iwanaga–Gorenstein [10] and so their modules have such covers. In particular, modules over integral group rings of finite groups have these covers. In this article we initiate a study of these covers over these group rings. To do so we study the so-called Gorenstein cotorsion modules, i.e. the modules that split under Gorenstein flat modules. When the ring is ℤ, these are just the usual cotorsion modules. Harrison [16] gave a complete characterization of torsion free cotorsion ℤ-modules. We show that with appropriate modifications Harrison's results carry over to integral group rings ℤG when G is finite. So we classify the Gorenstein cotorsion modules which are also Gorenstein flat over these ℤG. Using these results we classify modules that can be the kernels of Gorenstein flat covers of integral group rings of finite groups. In so doing we necessarily give examples of such covers. We use the tools we develop to associate an integer invariant n with every finite group G and prime p. We show 1≤n≤|G : P| where P is a Sylow p-subgroup of G and gives some indication of the significance of this invariant. We also use the results of the paper to describe the co-Galois groups associated to the Gorenstein flat cover of a ℤG-module. Presented by A. Verschoren Mathematics Subject Classifications (2000) 20C05, 16E65.     

Extension closure of relative syzygy modules

In this paper we introduce the notion of relative syzygy modules.We then study the extensionclosure of the category of modules consisting of relative syzygy modules(resp.relative k-torsionfree modules).     

On twisted representations of vertex algebras

In this paper, we develop a formalism for working with representations of vertex and conformal algebras by generalized fields—formal power series involving non-integer powers of the variable. The main application of our technique is the construction of a large family of representations for the vertex superalgebra corresponding to an integer lattice Λ. For an automorphism coming from a finite-order automorphism we find the conditions for existence of twisted modules of . We show that the category of twisted representations of is semisimple with finitely many isomorphism classes of simple objects.     

A Question of Nori: Projective Generation of Ideals

Let A be a smooth affine domain of dimension d over an infinite perfect field k and let n be an integer such that 2n d + 3. Let I A[T] be an ideal of height n. Assume that I = (f ₁,...,f _n ) + (I ² T). Under these assumptions, it is proved in this paper that I = (g ₁,...,g _n ) with f _i – g _i (I ² T), thus settling a question of Nori affirmatively.