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pro vyhledávání: '"22E65"'
Autor:
Henriques, André G., Tener, James E.
The Lie algebra of vector fields on $S^1$ integrates to the Lie group of diffeomorphisms of $S^1$. It is well known since the work of Segal and Neretin that there is no Lie group whose Lie algebra is the complexification of vector fields on $S^1$. A
Externí odkaz:
http://arxiv.org/abs/2410.05929
Autor:
Glockner, Helge, Suri, Ali
If G is a Lie group modeled on a Fr\'echet space, let e be its neutral element and g be its Lie algebra. We show that every strong ILB-Lie group G is L^1-regular in the sense that each f in L^1([0,1],g) is the right logarithmic derivative of some abs
Externí odkaz:
http://arxiv.org/abs/2410.02909
Autor:
Pelletier, Fernand, Cabau, Patrick
In this paper the notion of Dirac structure in finite dimension is extended to the convenient setting. In particular, we introduce the notion of partial Dirac structure on convenient Lie algebroids and manifolds. We then look for those structures who
Externí odkaz:
http://arxiv.org/abs/2409.13497
Autor:
Pinaud, Matthieu F.
For $p\in [1,\infty]$, we define a smooth manifold structure on the set of absolutely continuous functions $\gamma\colon [a,b]\to N$ with $L^p$-derivatives for each smooth manifold $N$ modeled on a sequentially complete locally convex topological vec
Externí odkaz:
http://arxiv.org/abs/2409.06512
In this short note we discuss the existence of singular points for the exponential function of a semidirect product Lie group close to $0$. As an application, we prove that the Bondi-Metzner-Sachs group of symmetries of an asymptotically flat spaceti
Externí odkaz:
http://arxiv.org/abs/2408.15053
We prove that autonomous Hamiltonian flows on the two-sphere exhibit the following dichotomy: the Hofer norm either grows linearly or is bounded in time by a universal constant C. Our approach involves a new technique, Hamiltonian symmetrization. Ess
Externí odkaz:
http://arxiv.org/abs/2408.08854
Autor:
Suri, Ali
This paper explores the application of central extensions of Lie groups and Lie algebras to derive the viscous quasi-geostrophic (QGS) equations, with and without Rayleigh friction term, on the torus as critical points of a stochastic Lagrangian. We
Externí odkaz:
http://arxiv.org/abs/2408.06159
Let $M$ be a convex polytope with non-empty interior in a finite dimensional vector space, such that each vertex of $M$ is contained in exactly $n$ edges of $M$. The Lie group of all smooth diffeomorphisms of $M$ contains the Lie subgroup of all diff
Externí odkaz:
http://arxiv.org/abs/2407.05444
We construct a smooth Banach manifold BV$([a,b], M)$ whose elements are suitably-defined functions $f:[a,b] \rightarrow M$ of bounded variation with values in a smooth Banach manifold $M$ which admits a local addition. If the target manifold is a Ban
Externí odkaz:
http://arxiv.org/abs/2407.05190
We pioneer the development of a rigorous infinite-dimensional framework for the Kempf-Ness theorem, addressing the significant challenge posed by the absence of a complexification for the symmetry group in infinite dimensions, e.g, the diffeomorphism
Externí odkaz:
http://arxiv.org/abs/2405.20864