Lyubeznik's Resolution and Rooted Complexes

We describe a new family of free resolutions for a monomial ideal I, generalizing Lyubeznik's construction. These resolutions are cellular resolutions supported on the rooted complexes of the lcm-lattice of I. Our resolutions are minimal for the matroid ideal of a finite projective space.     

Nuclear dimension, $$\mathcal{ }$$-stability,and algebraic simplicity for stably projectionless $$C^*$$C∗-algebras

Procesi bundles are certain vector bundles on symplectic resolutions of quotient singularities for wreath-products of the symmetric groups with the Kleinian groups. Roughly speaking, we can define Procesi bundles as bundles on resolutions that provide derived McKay equivalence. In this paper we classify Procesi bundles on resolutions obtained by Hamiltonian reduction and relate the Procesi bundles to the tautological bundles on the resolutions. Our proofs are based on deformation arguments and a connection of Procesi bundles with symplectic reflection algebras.     

Virtual criterion for generalized Eagon-Northcott complexes

Given any map of finitely generated free modules, Buchsbaum and Eisenbud define a family of generalized Eagon-Northcott complexes associated to it [3]. We give sufficient criterion for these complexes to be virtual resolutions, thus adding to the known examples of virtual resolutions, particularly those not coming from minimal free resolutions.     

On free resolutions of some semigroup rings

For some numerical semigroup rings of small embedding dimension, namely those of embedding dimension 3, and symmetric or pseudosymmetric of embedding dimension 4, presentations has been determined in the literature. We extend these results by giving the whole graded minimal free resolutions explicitly. Then we use these resolutions to determine some invariants of the semigroups and certain interesting relations among them. Finally, we determine semigroups of small embedding dimensions which have strongly indispensable resolutions.     

A characteristic-free example of a Lascoux resolution, and letter-place methods for intertwining numbers

An example is given to show the relationship between characteristic-free resolutions and Lascoux resolutions of Weyl modules. We also give an indication of use of letter-place methods for the calculation of intertwining numbers.     

Palindromic Resolutions of Simple Modules

For a finite dimensional hereditary k-algebra H of Dynkin type, it is known that the trivial extension T(H) has the property that minimal projective resolutions of T(H)-modules are periodic. We examine conditions in which T(H)-modules have additional symmetry in their resolutions—namely, their resolutions are “palindromic.” A more general framework in which “palindromic” resolutions occur is also presented.     

Shapes of free resolutions over a local ring

We classify the possible shapes of minimal free resolutions over a regular local ring. This illustrates the existence of free resolutions whose Betti numbers behave in surprisingly pathological ways. We also give an asymptotic characterization of the possible shapes of minimal free resolutions over hypersurface rings. Our key new technique uses asymptotic arguments to study formal ${\mathbb {Q}}$ -Betti sequences.     

Essential norms and weak compactness of integration operators

The aim of this paper is to present a general method to construct projective resolutions of globally defined Mackey functors over a field of characteristic zero and apply it to obtain explicit resolutions for inflation functors. Our method is a special case of Bouc’s method in (Proc. Symp. Pure Math. 63 (1998), 31–84) and uses global Mackey functors to construct the projective resolutions.     

Characteristic-free resolutions of Weyl and Specht modules

We construct explicit resolutions of Weyl modules by divided powers and of co-Specht modules by permutational modules. We also prove a conjecture by Boltje and Hartmann (2010) [7] on resolutions of co-Specht modules.     

Gerstenhaber brackets on Hochschild cohomology of general twisted tensor products

We present techniques for computing Gerstenhaber brackets on Hochschild cohomology of general twisted tensor product algebras. These techniques involve twisted tensor product resolutions and are based on recent results on Gerstenhaber brackets expressed on arbitrary bimodule resolutions.     

Projective resolutions up to bounded torsion and bounds for the orders of the finite subgroups

We prove that group (co)homology can be computed up to bounded torsion using certain generalized projective resolutions. We investigate the notion of dimension obtained using this kind of resolutions and its relationship with the existence of torsion in both ordinary and complete cohomology groups.     

Polygraphic resolutions and homology of monoids

We prove that for any monoid M, the homology defined by the second author by means of polygraphic resolutions coincides with the homology classically defined by means of resolutions by free ZM-modules.     

Betti-linear ideals

We introduce the notion of a Betti-linear monomial ideal, which generalizes the notion of lattice-linear monomial ideal introduced by Clark. We provide a characterization of Betti-linearity in terms of Tchernev's poset construction. As an application we obtain an explicit canonical construction for the minimal free resolutions of monomial ideals having pure resolutions.     

Koszulity of Algebras with Nonpure Resolutions

We discuss certain homological properties of graded algebras whose trivial modules admit nonpure resolutions. Such algebras include both of Artin–Schelter regular algebras of types (12221) and (13431). Under certain conditions, a module with nonpure resolution is decomposed to form an extension by two modules with pure resolutions.     

小波理论在无单元方法中权函数研究的应用

小波理论中多分辨率分析(MRA),可以提供在不同分辨率下分析表达信息的有效途径．基于样条小波多分辨率分析,将无单元中的权函数投影到尺度空间去研究,尝试一种新的权函数研究方法,并给出了算例．     

Cohomology pairings on singular quotients in geometric invariant theory

In this paper we shall give formulas for the pairings of intersection cohomology classes of complementary dimensions in the intersection cohomology of geometric invariant-theoretic quotients for which semistability is not necessarily the same as stability (although we make some weaker assumptions on the action). We also give formulas for intersection pairings on resolutions of singularities (or more precisely partial resolutions, since orbifold singularities are allowed) of the quotients.     

Some resolutions of S(5, 8, 24)

There exist 13 mutually disjoint resolutions of the Steiner system S(5, 8, 24). There also exist nine nonisomorphic mutually disjoint resolutions of S(5, 8, 24) where three of the resolutions have the same L₂(23) as an automorphism group and the other six have the same affine group C₂₃¹¹ as an automorphism group. A resolution of S(5, 8, 24) using a group of order 21 is displayed and a 13-dimensional Room-type design is mentioned.     

Résolution d'EDP par un schéma en temps «pararéel »

The purpose of this Note is to propose a time discretization of a partial differential evolution equation that allows for parallel implementations. The method, based on an Euler scheme, combines coarse resolutions and independent fine resolutions in time in the same spirit as standard spacial approximations. The resulting parallel implementation is done in the non standard time direction. Its main goal concerns real time problems, hence the proposed terminology of “parareal” algorithm.