https://www.mscand.dk/issue/feed MATHEMATICA SCANDINAVICA 2020-04-06T03:48:40+02:00 Andrew Swann mscand@math.au.dk Open Journal Systems https://www.mscand.dk/article/view/114969 Low-dimensional bounded cohomology and extensions of groups 2020-04-06T03:48:40+02:00 Nicolaus Heuer mscand@math.au.dk <p>Bounded cohomology of groups was first studied by Gromov in 1982 in his seminal paper M.&nbsp;Gromov, <em>Volume and bounded cohomology</em>, Inst. Hautes Études Sci. Publ. Math. (1982), no.&nbsp;56, 5–99. Since then it has sparked much research in Geometric Group Theory. However, it is notoriously hard to explicitly compute bounded cohomology, even for most basic “non-positively curved” groups. On the other hand, there is a well-known interpretation of <em>ordinary</em> group cohomology in dimension $2$ and $3$ in terms of group extensions. The aim of this paper is to make this interpretation available for <em>bounded</em> group cohomology. This will involve <em>quasihomomorphisms</em> as defined and studied by K.&nbsp;Fujiwara and M.&nbsp;Kapovich, <em>On quasihomomorphisms with noncommutative targets</em>, Geom. Funct. Anal. 26 (2016), no.&nbsp;2, 478–519.</p> 2020-03-29T00:00:00+01:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/115970 Hopf algebra actions and transfer of Frobenius and symmetric properties 2020-04-06T03:48:29+02:00 S. Dăscălescu mscand@math.au.dk C. Năstăsescu mscand@math.au.dk L. Năstăsescu mscand@math.au.dk <p>If $H$ is a finite-dimensional Hopf algebra acting on a finite-dimensional algebra $A$, we investigate the transfer of the Frobenius and symmetric properties through the algebra extensions $A^H\subset A\subset A\mathbin{\#} H$.</p> 2020-03-29T00:00:00+01:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/116681 The weak Lefschetz property for quotients by quadratic monomials 2020-04-06T03:48:05+02:00 Juan Migliore mscand@math.au.dk Uwe Nagel mscand@math.au.dk Hal Schenck mscand@math.au.dk <p>Michałek and Miró-Roig, in J. Combin. Theory Ser.&nbsp;A 143 (2016), 66–87, give a beautiful geometric characterization of Artinian quotients by ideals generated by quadratic or cubic monomials, such that the multiplication map by a general linear form fails to be injective in the first nontrivial degree. Their work was motivated by conjectures of Ilardi and Mezzetti, Miró-Roig and&nbsp;Ottaviani, connecting the failure to Laplace equations and classical results of Togliatti on osculating planes. We study quotients by quadratic monomial ideals, explaining failure of the Weak Lefschetz Property for some cases not covered by Michałek and&nbsp;Miró-Roig.</p> 2020-03-29T00:00:00+01:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/117703 New characterizations of spacelike hyperplanes in the steady state space 2020-04-06T03:47:59+02:00 Cícero P. Aquino mscand@math.au.dk Halyson I. Baltazar mscand@math.au.dk Henrique F. de Lima mscand@math.au.dk <p>In this article, we deal with complete spacelike hypersurfaces immersed in an open region of the de Sitter space $\mathbb {S}^{n+1}_{1}$ which is known as the steady state space $\mathcal {H}^{n+1}$. Under suitable constraints on the behavior of the higher order mean curvatures of these hypersurfaces, we are able to prove that they must be spacelike hyperplanes of $\mathcal {H}^{n+1}$. Furthermore, through the analysis of the hyperbolic cylinders of $\mathcal {H}^{n+1}$, we discuss the importance of the main hypothesis in our results. Our approach is based on a generalized maximum principle at infinity for complete Riemannian manifolds.</p> 2020-03-29T00:00:00+01:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/115971 Theta-regularity and log-canonical threshold 2020-04-06T03:48:23+02:00 Morten Øygarden mscand@math.au.dk Sofia Tirabassi mscand@math.au.dk <p>We show that an inequality, proven by Küronya-Pintye, which governs the behavior of the log-canonical threshold of an ideal over $\mathbb {P}^n$ and that of its Castelnuovo-Mumford regularity, can be applied to the setting of principally polarized abelian varieties by substituting the Castelnuovo-Mumford regularity with Θ-regularity of Pareschi-Popa.</p> 2020-03-29T00:00:00+01:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/115624 Some operator inequalities for Hermitian Banach $*$-algebras 2020-04-06T03:48:34+02:00 Hamed Najafi mscand@math.au.dk <p>In this paper, we extend the Kubo-Ando theory from operator means on C$^{*}$-algebras to a Hermitian Banach $*$-algebra $\mathcal {A}$ with a continuous involution. For this purpose, we show that if $a$ and $b$ are self-adjoint elements in $\mathcal {A}$ with spectra in an interval $J$ such that $a \leq b$, then $f(a) \leq f(b)$ for every operator monotone function $f$ on $J$, where $f(a)$ and $f(b)$ are defined by the Riesz-Dunford integral. Moreover, we show that some convexity properties of the usual operator convex functions are preserved in the setting of Hermitian Banach $*$-algebras. In particular, Jensen's operator inequality is presented in these cases.</p> 2020-03-29T00:00:00+01:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/116147 Noncommutative coverings of quantum tori 2020-04-06T03:48:16+02:00 Kay Schwieger mscand@math.au.dk Stefan Wagner mscand@math.au.dk <p>We investigate a framework for coverings of noncommutative spaces. Furthermore, we study noncommutative coverings of irrational quantum tori and characterize all such coverings that are connected in a reasonable sense.</p> 2020-03-29T00:00:00+01:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/116243 Stability analysis of a delay differential Kaldor's model with government policies 2020-04-06T03:48:10+02:00 Tomás Caraballo mscand@math.au.dk Alex Pereira da Silva mscand@math.au.dk <p>This paper is devoted to analysis of the stability of the economy according to an extended version of Kaldor's economic growth model. We consider the role of the government and its simultaneous monetary and fiscal policies and we study whether or not a time delay between the recognition and the implementation of its fiscal policy can affect the economic stability. Numerical simulations provide further conclusions about the long-term behavior of the four variables modeled—namely, national income, capacity of production, bonds value and money supply.</p> 2020-03-29T00:00:00+01:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/119120 Backward shift invariant subspaces in reproducing kernel Hilbert spaces 2020-04-06T03:47:53+02:00 Emmanuel Fricain mscand@math.au.dk Javad Mashreghi mscand@math.au.dk Rishika Rupam mscand@math.au.dk <p>In this note, we describe the backward shift invariant subspaces for an abstract class of reproducing kernel Hilbert spaces. Our main result is inspired by a result of Sarason concerning de Branges-Rovnyak spaces (the non-extreme case). Furthermore, we give new applications in the context of the range space of co-analytic Toeplitz operators and sub-Bergman spaces.</p> 2020-03-29T00:00:00+01:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/119679 Issue covers 2020-03-29T18:36:15+02:00 Mathematica Scandinavica mscand@math.au.dk <p>Issue covers</p> 2020-03-29T00:00:00+01:00 ##submission.copyrightStatement## https://www.mscand.dk/article/view/119680 Volume title pages 2020-03-29T18:38:14+02:00 Mathematica Scandinavica mscand@math.au.dk <p>Volume title pages</p> 2020-03-29T00:00:00+01:00 ##submission.copyrightStatement##