The coarse moduli space of a flat analytic groupoid

Annali di Matematica Pura ed Applicata (1923 -) - Let $$\mathcal X $$ be a flat analytic groupoid $$R_X\stackrel{s}{\underset{t}{\rightrightarrows }}X$$ such that the holomorphic map...     

Generation in singularity categories of hypersurfaces of countable representation type

The Orlov spectrum and Rouquier dimension are invariants of a triangulated category to measure how big the category is, and they have been studied actively. In this paper, we investigate the singularity category $$\textsf {D} _{\textsf {sg} }(R)$$ of a hypersurface R of countable representation type. For a thick subcategory $${\mathcal {T}}$$ of $$\textsf {D} _{\textsf {sg} }(R)$$ and a full subcategory $$\mathcal {X}$$ of $${\mathcal {T}}$$, we calculate the Rouquier dimension of $${\mathcal {T}}$$ with respect to $$\mathcal {X}$$. Furthermore, we prove that the level in $$\textsf {D} _{\textsf {sg} }(R)$$ of the residue field of R with respect to each nonzero object is at most one.     

The minimum principle for affine functions and isomorphisms of continuous affine function spaces

Let X be a compact convex set and let ext X stand for the set of extreme points of X. We show that if $$f:X\rightarrow {\mathbb {R}}$$ is an affine function with the point of continuity property such that $$f\le 0$$ on $${\text {ext}}\,X$$, then $$f\le 0$$ on X. As a corollary of this minimum principle, we obtain a generalization of a theorem by C.H. Chu and H.B. Cohen by proving the following result. Let X, Y be compact convex sets such that every extreme point of X and Y is a weak peak point and let $$T:\mathfrak {A}^c(X)\rightarrow \mathfrak {A}^c(Y)$$ be an isomorphism such that $$\left\| T\right\| \cdot \left\| T^{-1}\right\| <2$$. Then $${\text {ext}}\,X$$ is homeomorphic to $${\text {ext}}\,Y$$.     

The Lawson number of a semitopological semilattice

Semigroup Forum - For a Hausdorff topologized semilattice X its Lawson number $$\bar{\Lambda }(X)$$ is the smallest cardinal $$\kappa $$ such that for any distinct points $$x,y\in X$$ there exists...     

Homotopy Categories for Simply Connected Torsion Spaces

For each n > 1 and each multiplicative closed set of integers S, we study closed model category structures on the pointed category of topological spaces, where the classes of weak equivalences are classes of maps inducing isomorphism on homotopy groups with coefficients in determined torsion abelian groups, in degrees higher than or equal to n. We take coefficients either on all the cyclic groups with s ∈ S, or in the abelian group where is the group of fractions of the form with s ∈ S. In the first case, for n > 1 the localized category is equivalent to the ordinary homotopy category of (n − 1)-connected CW-complexes whose homotopy groups are S-torsion. In the second case, for n > 1 we obtain that the localized category is equivalent to the ordinary homotopy category of (n − 1)-connected CW-complexes whose homotopy groups are S-torsion and the nth homotopy group is divisible. These equivalences of categories are given by colocalizations , obtained by cofibrant approximations on the model structures. These colocalization maps have nice universal properties. For instance, the map is final (in the homotopy category) among all the maps of the form Y → X with Y an (n − 1)-connected CW-complex whose homotopy groups are S-torsion and its nth homotopy group is divisible. The spaces , are constructed using the cones of Moore spaces of the form M(T, k), where T is a coefficient group of the corresponding structure of models, and homotopy colimits indexed by a suitable ordinal. If S is generated by a set P of primes and S ^p is generated by a prime p ∈ P one has that for n > 1 the category is equivalent to the product category . If the multiplicative system S is generated by a finite set of primes, then localized category is equivalent to the homotopy category of n-connected Ext-S-complete CW-complexes and a similar result is obtained for .     

The Monge Problem in Banach Spaces

In this paper, we generalize the Kantorovich functional to K?the-spaces for a cost or a profit function. We examine the convergence of probabilities with respect to this functional for some K?the-spaces. We study the Monge problem: Let be a K?the-space, P and Q two Borel probabilities defined on a Polish space M and a cost function . A K?the functional is defined by (P, Q) = inf where is the law of X. If c is a profit function, we note . (P, Q) = sup Under some conditions, we show the existence of a Monge function, φ, such that , or .      

Anti-derivable linear maps at zero on standard operator algebras

Acta Mathematica Hungarica - Let $$\mathcal{X}$$ be a complex Banach space with $$\dim \mathcal{X}\geq 2$$ , and $$\mathcal{A} \subseteq \mathcal{B}(\mathcal{X})$$ be a standard operator algebra....     

Maps preserving a certain product of operators

Let $$\mathcal {A}$$ be a standard operator algebra on a Banach space $$\mathcal {X}$$ with $$ \dim \mathcal {X}\ge 3$$. In this paper, we determine the form of the bijective maps $$\phi :\mathcal {A}\longrightarrow \mathcal {A}$$ satisfying $$\begin{aligned} \phi \left( \frac{1}{2}(AB^2+B^2A)\right) = \frac{1}{2}[\phi (A)\phi (B)^{2}+\phi (B)^{2}\phi (A)], \end{aligned}$$for every $$A,B \in \mathcal {A}$$.     

Near coverings and cosystolic expansion

Archiv der Mathematik - Let X,&nbsp;Y be simplicial complexes and let $$f:Y \rightarrow X$$ be a simplicial surjective map. We introduce a notion of deficiency of f, denoted by $$m_f(Y)$$ ,...     

The asymptotic of curvature of direct image bundle associated with higher powers of a relatively ample line bundle

Geometriae Dedicata - Let $$\pi :\mathcal {X}\rightarrow M$$ be a holomorphic fibration with compact fibers and L a relatively ample line bundle over $$\mathcal {X}$$ . We obtain the asymptotic of...     

Monogenic dihedral quartic extensions

The Ramanujan Journal - In this paper, we prove that the number of monogenic dihedral quartic extensions of absolute discriminants $$\le X$$ is of size $$O(X^{\frac{3}{4}}(\log X)^3)$$ .     

Reduced Minimum Modulus Preserving in Banach Space

Let be the algebra of all bounded linear operators on a complex Banach space X and γ(T) be the reduced minimum modulus of operator . In this work, we prove that if , is a surjective linear map such that is an invertible operator, then , for every , if and only if, either there exist two bijective isometries and such that for every , or there exist two bijective isometries and such that for every . This generalizes for a Banach space the Mbekhta’s theorem [12].      

Crossed Modules and Quantum Groups in Braided Categories

Let A be a Hopf algebra in a braided category . Crossed modules over A are introduced and studied as objects with both module and comodule structures satisfying a compatibility condition. The category of crossed modules is braided and is a concrete realization of a known general construction of a double or center of a monoidal category. For a quantum braided group the corresponding braided category of modules is identified with a full subcategory in . The connection with cross products is discussed and a suitable cross product in the class of quantum braided groups is built. Majid–Radford theorem, which gives equivalent conditions for an ordinary Hopf algebra to be such a cross product, is generalized to the braided category. Majid's bosonization theorem is also generalized.     

Coreflections Versus Regular Epimorphisms in Categories of Topological Spaces

Let be an epireflective subcategory of the category Top of topological spaces which is not contained in the category of indiscrete spaces (e.g. Top, the category of Hausdorff spaces, the category of Tychonoff spaces) and be a coreflective subcategory of . In this paper we prove that the coreflector preserves regular epimorphisms if and only if or is contained in the category of discrete spaces.     

Kaplansky classes and derived categories

We put a monoidal model category structure on the category of chain complexes of quasi-coherent sheaves over a quasi-compact and semi-separated scheme X. The approach generalizes and simplifies the method used by the author in (Trans Am Math Soc 356(8) 3369–3390, 2004) and (Trans Am Math Soc 358(7), 2855–2874, 2006) to build monoidal model structures on the category of chain complexes of modules over a ring and chain complexes of sheaves over a ringed space. Indeed, much of the paper is dedicated to showing that in any Grothendieck category , any nice enough class of objects induces a model structure on the category Ch() of chain complexes. The main technical requirement on is the existence of a regular cardinal κ such that every object satisfies the following property: Each κ-generated subobject of F is contained in another κ-generated subobject S for which . Such a class is called a Kaplansky class. Kaplansky classes first appeared in Enochs and López-Ramos (Rend Sem Mat Univ Padova 107, 67–79, 2002) in the context of modules over a ring R. We study in detail the connection between Kaplansky classes and model categories. We also find simple conditions to put on which will guarantee that our model structure is monoidal. We will see that in several categories the class of flat objects form such Kaplansky classes, and hence induce monoidal model structures on the associated chain complex categories. We will also see that in any Grothendieck category , the class of all objects is a Kaplansky class which induces the usual (non-monoidal) injective model structure on Ch().     

Idempotent Completion of n-Angulated Categories

Applied Categorical Structures - Let $${\mathcal {C}}$$ be an n-angulated category. We prove that its idempotent completion $$\widetilde{{\mathcal {C}}}$$ admits a unique n-angulated structure such...     

On restricted functional inequalities associated with quadratic functional equations

Aequationes mathematicae - In this paper it is proved that, for a function $$f:\mathcal {X}\rightarrow E$$ mapping from a normed linear space $$\mathcal {X}$$ into an inner product space E, the...     

The Quasiapproximate $(\mathcal{U} + \mathcal{K})$ –Invariants of Essentially Normal Operators

For a class of essentially normal operators, we characterize their norm closures of –orbits. Moreover, we introduce a notion of the quasiapproximate – equivalence of essentially normal operators and determine completely the quasiapproximate –invariants. Finally, we give the canonical forms of essentially normal operators under this quasiapproximate –equivalence.     

C*-Modular Vector States

Let be a C*-algebra and X a Hilbert C* -module. If is a projection, let be the p-sphere of X. For φ a state of with support p in and consider the modular vector state φ_x of given by The spheres provide fibrations