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We study the gauge symmetries in a Mielke-Baekler type model of gravity in 2+1 dimensions. The model is built in a Poincare gauge theory framework where localisation of Poincare symmetries lead to gravity. However, explicit construction of…

General Relativity and Quantum Cosmology · Physics 2012-12-19 Rabin Banerjee , Debraj Roy

In this paper we consider a construction in an arbitrary triangulated category T which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of T satisfying some finite tilting assumptions, we…

Category Theory · Mathematics 2010-06-03 David Pauksztello

We prove a sheaf-theoretic derived-category generalization of Greenlees-May duality (a far-reaching generalization of Grothendieck's local duality theorem): for a quasi-compact separated scheme X and a "proregular" subscheme Z---for…

alg-geom · Mathematics 2008-02-03 Leovigildo Alonso , Ana Jeremías , Joseph Lipman

Motivated by duality phenomena for derived global sections on derived local systems on compact oriented manifolds, we introduce the notion of a $d$-duality context between symmetric monoidal enriched categories. In this setting, the right…

Category Theory · Mathematics 2026-04-02 Valerio Melani , Hugo Pourcelot

Duality symmetries of supergravity theories are powerful tools to restrict the number of possible actions, to link different dimensions and number of supersymmetries and might help to control quantisation. (Hodge-Dirac-)Dualisation of gauge…

High Energy Physics - Theory · Physics 2007-05-23 B. L. Julia

Einstein's theory in the vacuum was recently shown to possess an $SO(2)$ duality invariance, which is broken by coupling to matter. Duality invariance can be restored by enlarging the phase space of the theory to allow for violations of the…

High Energy Physics - Theory · Physics 2023-11-15 Uri Kol , Shing-Tung Yau

The dual Gromov-Hausdorff propinquity is a generalization of the Gromov-Hausdorff distance to the class of Leibniz quantum compact metric spaces, designed to be well-behaved with respect to C*-algebraic structures. In this paper, we present…

Operator Algebras · Mathematics 2018-03-20 Frederic Latremoliere

A geometric interpretation of the duality between two real forms of the complex trigonometric Ruijsenaars-Schneider system is presented. The phase spaces of the systems in duality are viewed as two different models of the same reduced phase…

Mathematical Physics · Physics 2011-01-04 L. Feher , C. Klimcik

We describe how to approximate the Riemann curvature tensor as well as sectional curvatures on possibly infinite-dimensional shape spaces that can be thought of as Riemannian manifolds. To this end, we extend the variational time…

Numerical Analysis · Mathematics 2019-12-17 Alexander Effland , Behrend Heeren , Martin Rumpf , Benedikt Wirth

We introduce and analyze a Spencer-type elliptic complex on the space of differential forms valued in symmetric powers of an adjoint bundle, $\Omega^\bullet(X)\otimes \mathrm{Sym}^\bullet(G)$. The complex is governed by a total differential…

General Mathematics · Mathematics 2025-09-30 Dongzhe Zheng

Premetrics and premetrisable spaces have been long studied and their topological interrelationships are well-understood. Consider the category ${\bf Pre}$ of premetric spaces and $\epsilon$-$\delta$ continuous functions as morphisms. The…

Category Theory · Mathematics 2016-11-03 J. Bruno , P. Szeptycki

We prove a correspondence, for Riemannian manifolds with self-dual Weyl tensor, between twistor functions and solutions to the Teukolsky equations for any conformal and spin weights. In particular, we give a contour integral formula for…

General Relativity and Quantum Cosmology · Physics 2024-07-16 Bernardo Araneda

In the recent paper "The Nakayama functor and its completion for Gorenstein algebras", a class of Gorenstein algebras over commutative noetherian rings was introduced, and duality theorems for various categories of representations were…

Representation Theory · Mathematics 2023-03-10 Wassilij Gnedin , Srikanth B. Iyengar , Henning Krause

Let T be a Hom-finite triangulated Krull-Schmidt category over a field k. Inspired by a definition of Koenig and Liu, we say that a family S of pairwise orthogonal objects in T with trivial endomorphism rings is a simple-minded system if…

Representation Theory · Mathematics 2016-06-07 Alex Dugas

We study the tensor-triangular geometry of the category of equivariant $G$-spectra for $G$ a profinite group, $\mathsf{Sp}_G$. Our starting point is the construction of a ``continuous'' model for this category, which we show agrees with all…

Algebraic Topology · Mathematics 2024-01-04 Scott Balchin , David Barnes , Tobias Barthel

The Euler-Gauss linear transformation formula for the hypergeometric function was extended by Goursat for the case of logarithmic singularities. By replacing the perturbed Bessel differential equation by a monodromic functional equation,…

Classical Analysis and ODEs · Mathematics 2015-10-01 V. P. Gurarii , D. W. H. Gillam

We introduce the dual Koenigs lattices, which are the integrable discrete analogues of conjugate nets with equal tangential invariants, and we find the corresponding reduction of the fundamental transformation. We also introduce the notion…

Exactly Solvable and Integrable Systems · Physics 2009-11-10 A. Doliwa , M. Nieszporski , P. M. Santini

We give a category theoretic approach to several known equivalences from (classic) tilting theory and commutative algebra. Furthermore, we apply our main results to establish a duality theory for relative Cohen-Macaulay modules in the sense…

Commutative Algebra · Mathematics 2017-10-25 Olgur Celikbas , Henrik Holm

Random tensor models for a generic complex tensor generalize matrix models in arbitrary dimensions and yield a theory of random geometries. They support a 1/N expansion dominated by graphs of spherical topology. Their Schwinger Dyson…

High Energy Physics - Theory · Physics 2015-06-04 Razvan Gurau

We prove that a finite dimensional algebra $A$ with representation-finite subcategory consisting of modules that are semi-Gorenstein-projective and $n$-th syzygy modules is left weakly Gorenstein. This generalises a theorem of Ringel and…

Representation Theory · Mathematics 2021-09-03 Rene Marczinzik