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Authors:Arman Sarikyan Abstract: International Journal of Mathematics, Volume 33, Issue 05, April 2022. We classify toric Fano threefolds having at worst terminal singularities such that the rank of the [math]-invariant part of the class group equals one, where [math] is a finite group acting on the variety by automorphisms. Citation: International Journal of Mathematics PubDate: 2022-04-25T07:00:00Z DOI: 10.1142/S0129167X22500343 Issue No:Vol. 33, No. 05 (2022)

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Authors:Luca Giorgetti Abstract: International Journal of Mathematics, Volume 33, Issue 05, April 2022. Let [math] be a unital inclusion of arbitrary von Neumann algebras. We give a 2-[math]-categorical/planar algebraic description of normal faithful conditional expectations [math] with finite index and their duals [math] by means of the solutions of the conjugate equations for the inclusion morphism [math] and its conjugate morphism [math]. In particular, the theory of index for conditional expectations admits a 2-[math]-categorical formulation in full generality. Moreover, we show that a pair [math] as above can be described by a Q-system, and vice versa. These results are due to Longo in the subfactor/simple tensor unit case [R. Longo, Index of subfactors and statistics of quantum fields. II. Correspondences, braid group statistics and Jones polynomial, Comm. Math. Phys. 130(1990) 285–309; A duality for Hopf algebras and for subfactors. I, Comm. Math. Phys. 159 (1994) 133–150]. Citation: International Journal of Mathematics PubDate: 2022-04-25T07:00:00Z DOI: 10.1142/S0129167X22500379 Issue No:Vol. 33, No. 05 (2022)

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Authors:Xavier Roulleau Abstract: International Journal of Mathematics, Ahead of Print. Nikulin [On the quotient groups of the automorphism groups of hyperbolic forms by the subgroups generated by 2 reflections, J. Soviet. Math. 22 (1983) 1401–1476; Surfaces of type K3 with a finite automorphism group and a Picard group of rank three, Proc. Steklov Institute of Math. (3) (1985) 131–155] and Vinberg [Classification of 2-reflective hyperbolic lattices of rank 4, Trans. Moscow Math. Soc. (2007) 39–66] proved that there are only a finite number of lattices of rank [math] that are the Néron–Severi lattice of projective K3 surfaces with a finite automorphism group. The aim of this paper is to provide a more geometric description of such K3 surfaces X, when these surfaces have moreover no elliptic fibrations. In that case, we show that such K3 surface is either a quartic with special hyperplane sections or a double cover of the plane branched over a smooth sextic curve which has special tangencies properties with some lines, conics or cuspidal cubic curves. We then study the converse, i.e. if the geometric description we obtained characterizes these surfaces. In four cases, the description is sufficient, in each of the four other cases, there is exactly another one possibility which we study. We obtain that at least five moduli spaces of K3 surfaces (among the eight we study) are unirational. Citation: International Journal of Mathematics PubDate: 2022-04-30T07:00:00Z DOI: 10.1142/S0129167X22500409

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Authors:Valentin Deaconu Abstract: International Journal of Mathematics, Ahead of Print. We introduce the [math]-algebra [math] generated by the Koopman representation [math] of an étale groupoid [math] acting on a measure space [math]. We prove that for a level transitive self-similar action [math] with [math] finite and [math] constant, there is an invariant measure [math] on [math] and that [math] is residually finite dimensional with a normalized self-similar trace. We also discuss [math]-fold similarities of Hilbert spaces in connection to representations of the graph algebra [math] and self-similar representations of [math] in connection to the Cuntz–Pimsner algebra [math]. Citation: International Journal of Mathematics PubDate: 2022-04-27T07:00:00Z DOI: 10.1142/S0129167X22500434

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Authors:A. G. Ghazanfari, M. Sababheh Abstract: International Journal of Mathematics, Ahead of Print. In this paper, using the contractive maps, we present some new interpolations between the Heinz and Heron operator means for unitarily invariant norms. Let [math] and [math] be two positive definite operators. and let [math], [math]. If [math] and [math], or if [math] and [math], then Hr(A,X,B) ≤ (1 − β)Hμ(A,X,B) + βHν(A,X,B) ≤ ℱα(A,X,B) . We also consider some Heinz-type inequalities that involve differences and sums of operators. We give new forms and reverse inequalities of the presented inequalities by Singh et al. Citation: International Journal of Mathematics PubDate: 2022-04-27T07:00:00Z DOI: 10.1142/S0129167X22500446

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Authors:Henan Wu, Lipeng Luo Abstract: International Journal of Mathematics, Ahead of Print. Both the basic cohomology groups and the reduced cohomology groups of the Schrödinger–Virasoro conformal algebra with trivial coefficients are completely determined. Citation: International Journal of Mathematics PubDate: 2022-04-25T07:00:00Z DOI: 10.1142/S0129167X22500410

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Authors:Uwe Semmelmann, Changliang Wang, M. Y.-K. Wang Abstract: International Journal of Mathematics, Ahead of Print. In this paper, we study the stability problem for the Einstein metrics on Sasaki Einstein and on complete nearly parallel [math] manifolds. In the Sasaki case we show linear instability if the second Betti number is positive. Similarly, we prove that nearly parallel [math] manifolds with positive third Betti number are linearly unstable. Moreover, we prove linear instability for the Berger space [math] which is a [math]-dimensional homology sphere with a proper nearly parallel [math] structure. Citation: International Journal of Mathematics PubDate: 2022-04-25T07:00:00Z DOI: 10.1142/S0129167X22500422

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Authors:Keshab Chandra Bakshi, Sruthymurali Abstract: International Journal of Mathematics, Ahead of Print. We describe the subfactor planar algebra of an intermediate subfactor [math] of an extremal subfactor [math] of finite Jones index which is not necessarily irreducible. Citation: International Journal of Mathematics PubDate: 2022-04-12T07:00:00Z DOI: 10.1142/S0129167X22500331

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Authors:Paul Herstedt Abstract: International Journal of Mathematics, Ahead of Print. We introduce a type of zero-dimensional dynamical system (a pair consisting of a totally disconnected compact metrizable space along with a homeomorphism of that space), which we call “fiberwise essentially minimal”, that is a class that includes essentially minimal systems and systems in which every orbit is minimal. We prove that the associated crossed product [math]-algebra of such a system is an A[math]-algebra. Under the additional assumption that the system has no periodic points, we prove that the associated crossed product [math]-algebra has real rank zero, which tells us that such [math]-algebras are classifiable by [math]-theory. The associated crossed product [math]-algebras to these nontrivial examples are of particular interest because they are non-simple (unlike in the minimal case). Citation: International Journal of Mathematics PubDate: 2022-04-12T07:00:00Z DOI: 10.1142/S0129167X22500355

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Authors:Indranil Biswas, Soumyadip Das, A. J. Parameswaran Abstract: International Journal of Mathematics, Ahead of Print. Let [math] be a separable finite surjective map between irreducible normal projective varieties defined over an algebraically closed field, such that the corresponding homomorphism between étale fundamental groups [math] is surjective. Fix a polarization on [math] and equip [math] with the pullback, by [math], of this polarization on [math]. Given a stable vector bundle [math] on [math], we prove that there is a vector bundle [math] on [math] with [math] isomorphic to [math] if and only if the direct image [math] contains a stable vector bundle [math] such that degree(F) rank(F) = 1 degree(f) ⋅degree(E) rank(E) . We also prove that [math] is stable for every stable vector bundle [math] on [math]. Citation: International Journal of Mathematics PubDate: 2022-04-12T07:00:00Z DOI: 10.1142/S0129167X22500392

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Authors:Yu Fang, Mengjie Zhang Abstract: International Journal of Mathematics, Ahead of Print. In this paper, using the method of blow-up analysis, the authors obtain an improved Trudinger–Moser inequality involving [math]-norm ([math]) and prove the existence of its extremal function on a closed Riemann surface [math] with the action of a finite isometric group [math]. To be exact, let [math] be the usual Sobolev space, a function space [math] and [math] [math] and [math] where [math] stands for the number of all distinct points in the set [math]. Define [math], where [math] is the standard [math]-norm on [math]. Using blow-up analysis, we prove that if [math], the supremum supu∈ℋG,∥∇gu∥22−α∥u∥p2≤1∫Σe4πℓu2dvg < +∞, and this supremum can be attained; if [math], the above supremum is infinite. This kind of inequality will play an important role in the study of prescribing Gaussian curvature problem and mean field equations. In particular, their result generalizes those of Chen [A Trudinger inequality on surfaces with conical singularities, Proc. Amer. Math. Soc. 108 (1990) 821–832], Yang [Extremal functions for Trudinger–Moser inequalities of Adimurthi–Druet type in dimension two, J. Differential Equations 258 (2015) 3161–3193] and Fang–Yang [Trudinger–Moser inequalities on a closed Riemannian surface with the action of a finite isometric group, Ann. Sc. Norm. Super. Pisa Cl. Sci. 20 (2020) 1295–1324]. Citation: International Journal of Mathematics PubDate: 2022-04-08T07:00:00Z DOI: 10.1142/S0129167X22500380

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Authors:Dušan Joksimović Abstract: International Journal of Mathematics, Ahead of Print. We prove that a closed manifold which admits a symplectic Lipschitz structure has non-vanishing even-degree cohomology groups with real coefficients. In particular, spheres [math] do not admit symplectic Lipschitz structures. Citation: International Journal of Mathematics PubDate: 2022-04-05T07:00:00Z DOI: 10.1142/S0129167X22500367