Let k be a field. Given two finite-dimensional right comodules N andM over a k–coalgebra C, the k–vector spaces ExtC(N,M) need not to be finite-dimensional. This is due to the fact that the injective right comodules appearing in the minimal injective resolution of M need not to be of finite dimension or even quasi-finite. The obstruction here is that factor comodules of quasi-finite comodules a...

We study the category of graded finite-dimensional representations of the polynomial current algebra associated to a simple Lie algebra. We prove that the category has enough injectives and compute the graded character of the injective envelopes of the simple objects as well as extensions betweeen simple objects. The simple objects in the category are parametized by the affine weight lattice. W...

We prove the existence of globally injective weak solutions in mixed boundary-value problems of second-gradient nonlinear elastostatics via energy minimization. This entails the treatment of self-contact. In accordance with the classical (first-gradient) theory, the model incorporates the unbounded growth of the potential energy density as the local volume ratio approaches zero. We work in a cl...

1 Definitions An orbifold is a Hausdorff space X0 along with an open cover {Ui} that is closed under finite intersection with the following properties. For each Ui there is an open set Ũi ⊆ R and a finite group Γi which acts on Ũi. In addition there is a homeomorphism φi : Ui ≈ Ũi/Γi and whenever Ui ⊂ Uj there is an injective homomorphism fij : Γi ↪→ Γj and Ũi can be embedded in Ũj such that th...

Let Λ be an Artinian algebra and F an additive subbifunctor of ExtΛ(−,−) having enough projectives and injectives. We prove that the dualizing subvarieties of mod Λ closed under F -extensions have F -almost split sequences. Let T be an F -cotilting module in mod Λ and S a cotilting module over Γ = End(T ). Then Hom(−, T ) induces a duality between F -almost split sequences in ⊥F T and almost sp...

This paper gives a proof that the universal cover of a closed 3-manifold built from three π1-injective handlebodies is homeomorphic to R. This construction is an extension to handlebodies of the conditions for gluing of three solid tori to produce non-Haken Seifert fibered manifolds with infinite fundamental group. This class of manifolds has been shown to contain non-Haken non-Seifert fibered ...

Let M be a closed oriented surface of genus g ≥ 1, let Bn(M) be the braid group of M on n strings, and let SBn(M) be the corresponding singular braid monoid. Our purpose in this paper is to prove that the desingularization map η : SBn(M) → Z[Bn(M)], introduced in the definition of the Vassiliev invariants (for braids on surfaces), is injective. AMS Subject Classification: Primary 20F36; Seconda...

We show that the Radon transform related to closed geodesics is injective on a Lie group if and only if the connected components are not homeomorphic to S nor to S. This is true for both smooth functions and distributions. The key ingredients of the proof are finding totally geodesic tori and realizing the Radon transform as a family of symmetric operators indexed by nontrivial homomorphisms fr...

In this paper we study the second Hochschild cohomology group HH(Λ) of a finite dimensional algebra Λ. In particular, we determine HH(Λ) where Λ is a finite dimensional self-injective algebra of finite representation type over an algebraically closed field K and show that this group is zero for most such Λ; we give a basis for HH(Λ) in the few cases where it is not zero.

Let τ be a hereditary torsion theory on the category R-Mod of left R-modules over an associative unitary ring R. We introduce the notion of τ-natural class as a class of modules closed under τ-dense submodules, direct sums, and τ-injective hulls. We study connections between certain conditions involving τ-(quasi-)injectivity in the context of τnatural classes, generalizing results established b...