| 1. |
- Andersson, Fredrik, et al.
(författare)
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Local existence of symmetric spinor potentials for symmetric (3,1)-spinors in Einstein space-times
- 2001
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Ingår i: Journal of Geometry and Physics. - 0393-0440 .- 1879-1662. ; 37:4, s. 273-290
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Tidskriftsartikel (refereegranskat)abstract
- We investigate the possibility of existence of a symmetric potential HABA'B'=H(AB)(A'B') for a symmetric (3,1)-spinor LABCA', e.g., a Lanczos potential of the Weyl spinor, as defined by the equation LABCA'=?(AB'H BC)A'B'. We prove that in all Einstein space-times such a symmetric potential HABA'B' exists. Potentials of this type have been found earlier in investigations of some very special spinors in restricted classes of space-times. A tensor version of this result is also given. We apply similar ideas and results by Illge to Maxwell's equations in a curved space-time. © 2001 Elsevier Science B.V.
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| 2. |
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| 3. |
- Abedin, Raschid, et al.
(författare)
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Classification of classical twists of the standard Lie bialgebra structure on a loop algebra
- 2021
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Ingår i: Journal of Geometry and Physics. - : Elsevier BV. - 0393-0440. ; 164
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Tidskriftsartikel (refereegranskat)abstract
- The standard Lie bialgebra structure on an affine Kac–Moody algebra induces a Lie bialgebra structure on the underlying loop algebra and its parabolic subalgebras. In this paper we classify all classical twists of the induced Lie bialgebra structures in terms of Belavin–Drinfeld quadruples up to a natural notion of equivalence. To obtain this classification we first show that the induced bialgebra structures are defined by certain solutions of the classical Yang–Baxter equation (CYBE) with two parameters. Then, using the algebro–geometric theory of CYBE, based on torsion free coherent sheaves, we reduce the problem to the well-known classification of trigonometric solutions given by Belavin and Drinfeld. The classification of twists in the case of parabolic subalgebras allows us to answer recently posed open questions regarding the so-called quasi-trigonometric solutions of CYBE.
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| 4. |
- Alho, A., et al.
(författare)
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A stellar model with diffusion in general relativity
- 2017
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Ingår i: Journal of Geometry and Physics. - : Elsevier BV. - 0393-0440. ; 120, s. 62-72
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Tidskriftsartikel (refereegranskat)abstract
- We consider a spherically symmetric stellar model in general relativity whose interior consists of a pressureless fluid undergoing microscopic velocity diffusion in a cosmological scalar field. We show that the diffusion dynamics compel the interior to be spatially homogeneous, by which one can infer immediately that within our model, and in contrast to the diffusion-free case, no naked singularities can form in the gravitational collapse. We then study the problem of matching an exterior Bondi type metric to the surface of the star and find that the exterior can be chosen to be a modified Vaidya metric with variable cosmological constant. Finally, we study in detail the causal structure of an explicit, self similar solution. (C) 2017 Elsevier B.V. All rights reserved.
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| 5. |
- Ames, Ellery, et al.
(författare)
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A class of solutions to the Einstein equations with AVTD behavior in generalized wave gauges
- 2017
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Ingår i: Journal of Geometry and Physics. - : Elsevier. - 0393-0440 .- 1879-1662. ; 121, s. 42-71
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Tidskriftsartikel (refereegranskat)abstract
- We establish the existence of smooth vacuum Gowdy solutions, which are asymptotically velocity term dominated (AVTD) and have T3-spatial topology, in an infinite dimensional family of generalized wave gauges. These results show that the AVTD property, which has so far been known to hold for solutions in areal coordinates only, is stable to perturbations of the coordinate systems. Our proof is based on an analysis of the singular initial value problem for the Einstein vacuum equations in the generalized wave gauge formalism, and provides a framework which we anticipate to be useful for more general spacetimes.
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| 6. |
- Arnlind, Joakim, et al.
(författare)
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Kahler-Poisson algebras
- 2019
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Ingår i: Journal of Geometry and Physics. - : ELSEVIER SCIENCE BV. - 0393-0440 .- 1879-1662. ; 136, s. 156-172
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Tidskriftsartikel (refereegranskat)abstract
- We introduce Kahler-Poisson algebras as analogues of algebras of smooth functions on Kahler manifolds, and prove that they share several properties with their classical counterparts on an algebraic level. For instance, the module of inner derivations of a Kahler-Poisson algebra is a finitely generated projective module, and allows for a unique metric and torsion-free connection whose curvature enjoys all the classical symmetries. Moreover, starting from a large class of Poisson algebras, we show that every algebra has an associated Kahler-Poisson algebra constructed as a localization. At the end, detailed examples are provided in order to illustrate the novel concepts. (C) 2018 Elsevier B.V. All rights reserved.
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| 7. |
- Arnlind, Joakim, et al.
(författare)
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Noncommutative minimal embeddings and morphisms of pseudo-Riemannian calculi
- 2021
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Ingår i: Journal of Geometry and Physics. - : ELSEVIER. - 0393-0440 .- 1879-1662. ; 159
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Tidskriftsartikel (refereegranskat)abstract
- In analogy with classical submanifold theory, we introduce morphisms of real metric calculi together with noncommutative embeddings. We show that basic concepts, such as the second fundamental form and the Weingarten map, translate into the noncommutative setting and, in particular, we prove a noncommutative analogue of Gauss equations for the curvature of a submanifold. Moreover, the mean curvature of an embedding is readily introduced, giving a natural definition of a noncommutative minimal embedding, and we illustrate the novel concepts by considering the noncommutative torus as a minimal surface in the noncommutative 3-sphere. (c) 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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| 8. |
- Arnlind, Joakim
(författare)
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Noncommutative Riemannian geometry of Kronecker algebras
- 2024
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Ingår i: Journal of Geometry and Physics. - : ELSEVIER. - 0393-0440 .- 1879-1662. ; 199
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Tidskriftsartikel (refereegranskat)abstract
- We study aspects of noncommutative Riemannian geometry of the path algebra arising from the Kronecker quiver with N arrows. To start with, the framework of derivation based differential calculi is recalled together with a discussion on metrics and bimodule connections compatible with the *-structure of the algebra. As an illustration, these concepts are applied to the noncommutative torus where examples of torsion free and metric (Levi-Civita) connections are given. In the main part of the paper, noncommutative geometric aspects of (generalized) Kronecker algebras are considered. The structure of derivations and differential calculi is explored, and torsion free bimodule connections are studied together with their compatibility with hermitian forms, playing the role of metrics on the module of differential forms. Moreover, for several different choices of Lie algebras of derivations, non -trivial Levi-Civita connections are constructed. (c) 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).
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| 9. |
- Arnlind, Joakim, et al.
(författare)
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On the Chern-Gauss-Bonnet theorem for the noncommutative 4-sphere
- 2017
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Ingår i: JOURNAL OF GEOMETRY AND PHYSICS. - : ELSEVIER SCIENCE BV. - 0393-0440. ; 111, s. 126-141
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Tidskriftsartikel (refereegranskat)abstract
- We construct a differential calculus over the noncommutative 4-sphere in the framework of pseudo-Riemannian calculi, and show that for every metric in a conformal class of perturbations of the round metric, there exists a unique metric and torsion-free connection. Furthermore, we find a localization of the projective module corresponding to the space of vector fields, which allows us to formulate a Chern-Gauss-Bonnet type theorem for the noncommutative 4-sphere. (C) 2016 Elsevier B.V. All rights reserved.
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| 10. |
- Bonechi, F., et al.
(författare)
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Equivariant Batalin-Vilkovisky formalism
- 2020
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Ingår i: Journal of Geometry and Physics. - : ELSEVIER. - 0393-0440 .- 1879-1662. ; 154
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Tidskriftsartikel (refereegranskat)abstract
- We study an equivariant extension of the Batalin-Vilkovisky formalism for quantizing gauge theories. Namely, we introduce a general framework to encompass failures of the quantum master equation, and we apply it to the natural equivariant extension of AKSZ solutions of the classical master equation (CME). As examples of the construction, we recover the equivariant extension of supersymmetric Yang-Mills in 2d and of Donaldson-Witten theory. (C) 2020 Elsevier B.V. All rights reserved.
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