Abstract We construct Grassmannian categories of infinite rank, providing an analogue the cluster introduced by Jensen, King, and Su. Each category rank is given as graded maximal Cohen–Macaulay modules over a certain hypersurface singularity. show that generically free $1$ in are bijection with Plücker coordinates appropriate algebra rank. Moreover, this structure preserving, it relates rigidi...

aim: abnormal joint mobility is an important factor in movement dysfunction and physical disability. a general lack of descriptive details exists for measurements of hip rotation range of motion (rom). this study was designed to establish the influence of hip position on active and passive range of motion of the hip in external and internal rotation(ext & int rot). material & methods: ...

We consider aane group schemes G over a eld k of characteristic p > 0. Equivalently , we consider nitely generated commutative k-algebras kG] (the coordinate algebra of G) endowed with the structure of a Hopf algebra. The group scheme G is said to be nite if kG] is nite dimensional (over k) and a nite group scheme is said to be innnitesimal if the ((nite dimensional) algebra kG] is local. A rat...

We prove that in a 2-Calabi-Yau triangulated category, each cluster tilting subcategory is Gorenstein with all its finitely generated projectives of injective dimension at most one. We show that the stable category of its Cohen-Macaulay modules is 3-CalabiYau. We deduce in particular that cluster-tilted algebras are Gorenstein of dimension at most one, and hereditary if they are of finite globa...

The main theorem of this paper complements the tame-wild dichotomy for commutative Noetherian rings, obtained by Klingler and Levy [14]–[16]. They gave a complete classification of all finitely generated modules over Dedekind-like rings (cf. Definition 1.1) and showed that, over any ring that is not a homomorphic image of a Dedekind-like ring, the category of finite-length modules has wild repr...

This result is strikingly similar to the following hoped-for picture of affine Lie algebra representation theory, explained to us by A.Beilinson. Let M1,M2 be two modules over an affine Lie algebra ĝ on the critical level. One hopes that there is a localization functor which associates to these modules perverse sheaves ∆(M1),∆(M2) over the semiinfinite flag space Ĝ/B̂. Suppose that ∆(M1) and ∆(M...

Let R be a hypersurface in an equicharacteristic or unramified regular local ring. For a pair of modules (M, N) over R we study applications of rigidity of Tor(M, N), based on ideas by Huneke, Wiegand and Jorgensen. We then focus on the hypersurfaces with isolated singularity and even dimension, and show that modules over such rings behave very much like those over regular local rings. Connecti...

Given a finite root system Φ, we show there is an integer c = c(Φ) such that dimExtG(L,L ) < c, for any reductive algebraic groupG with root system Φ and any irreducible rational G-modules L,L. We also prove that there is such a bound in the case of finite groups of Lie type, depending only on the root system and not on the underlying field. For quantum groups, we are able to obtain a similar r...