1,721,033 research outputs found
Metric compatibility and Levi-Civita connections on quantum groups
No full textArbitrary connections on a generic Hopf algebra H are studied and shown to extend to connections on tensor fields. On this ground a general definition of metric compatible connection is proposed. This leads to a sufficient criterion for the existence and uniqueness of the Levi-Civita connection, that of invertibility of an H-valued matrix. Provided invertibility for one metric, existence and uniqueness of the Levi-Civita connection for all metrics conformal to the initial one is proven. This class consists of metrics which are neither central (bimodule maps) nor equivariant, in general. For central and bicoinvariant metrics the invertibility condition is further simplified to a metric independent one. Examples include metrics on SLq(2)
On Curvature and Torsion in Courant Algebroids
No full textWe study the graded geometric point of view of curvature and torsion of Q-manifolds (differential graded manifolds). In particular, we get a natural graded geometric definition of Courant algebroid curvature and torsion, which correctly restrict to Dirac structures. Depending on an auxiliary affine connection K, we introduce the K-curvature and K-torsion of a Courant algebroid connection. These are conventional tensors on the body. Finally, we compute their Ricci and scalar curvature
Dispersion relations in κ-noncommutative cosmology
Full text linkWe study noncommutative deformations of the wave equation in curved backgrounds and discuss the modification of the dispersion relations due to noncommutativity combined with curvature of spacetime. Our noncommutative differential geometry approach is based on Drinfeld twist deformation, and can be implemented for any twist and any curved background. We discuss in detail the Jordanian twist - giving κ-Minkowski spacetime in flat space - in the presence of a Friedman-Lema tre-Robertson-Walker (FLRW) cosmological background. We obtain a new expression for the variation of the speed of light, depending linearly on the ratio E ph/E LV (photon energy/Lorentz violation scale), but also linearly on the cosmological time, the Hubble parameter and inversely proportional to the scale factor
Quantum Principal Bundles on Projective Bases
Full text linkThe purpose of this paper is to propose a sheaf theoretic approach to the theory of quantum principal bundles over non affine bases. We study noncommutative principal bundles corresponding to G→ G/ P, where G is a semisimple group and P a parabolic subgroup
Effetti dell’efficacia di un protocollo propedeutico al karate su alcuni parametri fisiologici in anziani istituzionalizzati
No full textCon l’invecchiamento l’organismo va incontro a dei cambiamenti che ne riducono la capacità di adattarsi all’ambiente, aumentando il rischio di infortuni e riducendone le aspettative di vita. Le degenerazioni strutturali a cui va maggiormente incontro l’anziano, sono i processi di perdita di massa ossea, la sarcopenia e il declino delle funzioni intellettive. Lo studio vuole valutare l’efficacia di due mesi di allenamento propedeutico al karate, e specificatamente della forma (kata), e verificarne l’influenza sui valori di forza, equilibrio, flessibilità e su alcuni parametri psicofisiologici (tasks attentive), confrontandolo con una normale attività di ginnastica per anziani
Non-commutative Einstein equations and Seiberg-Witten map
No full textThe Seiberg–Witten map is a powerful tool in non-commutative field theory, and it
has been recently obtained in the literature for gravity itself, to first order in noncommutativity.
This paper, relying upon the pure-gravity form of the action functional
considered in Ref. 2, studies the expansion to first order of the non-commutative Einstein
equations, and whether the Seiberg–Witten map can lead to a solution of such
equations when the underlying classical geometry is Schwarzschild. We find that, if one
first obtains the non-commutative field equations by varying the action of Ref. 2 with
respect to all non-commutative fields, and then tries to solve these equations by expressing
the non-commutative fields in terms of the commutative ones via Seiberg–Witten
map, no solution of these equations can be obtained when the commutative background
is Schwarzschild
Biomechanical Analysis Of Karate Techniques Based On The Evaluation Of The Body Kinetic Energy From 3D Mocap Data
No full textDifferential Calculi on Quantum Principal Bundles Over Projective Bases
Full text linkWe propose a sheaf-theoretic approach to the theory of differential calculi on quantum principal bundles over non-affine bases. After recalling the affine case we define differential calculi on sheaves of comodule algebras as sheaves of covariant bimodules together with a morphism of sheaves -the differential- such that the Leibniz rule and surjectivity hold locally. The main class of examples is given by covariant calculi over quantum flag manifolds, which we provide via an explicit Ore extension construction. In a second step we introduce principal covariant calculi by requiring a local compatibility of the calculi on the total sheaf, base sheaf and the structure Hopf algebra in terms of exact sequences. In this case Hopf–Galois extensions of algebras lift to Hopf–Galois extensions of exterior algebras with compatible differentials. In particular, the examples of principal (covariant) calculi on the quantum principal bundles Oq(SL2(C)) and Oq(GL2(C)) over the projective space P1(C) are discussed in detail
Topological t-duality for twisted tori
Full text linkWe apply the C∗-algebraic formalism of topological T-duality due to Mathai and Rosenberg to a broad class of topological spaces that include the torus bundles appearing in string theory compactifications with duality twists, such as nilmanifolds, as well as many other examples. We develop a simple procedure in this setting for constructing the T-duals starting from a commutative C∗-algebra with an action of Rn. We treat the general class of almost abelian solvmanifolds in arbitrary dimension in detail, where we provide necessary and sufficient criteria for the existence of classical T-duals in terms of purely group theoretic data, and compute them explicitly as continuous-trace algebras with non-trivial Dixmier– Douady classes. We prove that any such solvmanifold has a topological T-dual given by a C∗-algebra bundle of noncommutative tori, which we also compute explicitly. The monodromy of the original torus bundle becomes a Morita equivalence among the fiber algebras, so that these C∗-algebras rigorously describe the T-folds from non-geometric string theory.</p
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