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Reflection negative kernels and fractional Brownian motion

Autor: Jorgensen, P., Neeb, K. -H., Olafsson, G.

In this article we study the connection of fractional Brownian motion, representation theory and reflection positivity in quantum physics. We introduce and study reflection positivity for affine isometric actions of a Lie group on a Hilbert space E a

Externí odkaz: http://arxiv.org/abs/1805.02593

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Reflection positivity on real intervals

Autor: Jorgensen, P., Neeb, K. -H., Olafsson, G.

We study functions f : (a,b) ---> R on open intervals in R with respect to various kinds of positive and negative definiteness conditions. We say that f is positive definite if the kernel f((x + y)/2) is positive definite. We call f negative definite

Externí odkaz: http://arxiv.org/abs/1608.04010

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Reflection positive affine actions and stochastic processes

Autor: Jorgensen, P. E. T., Neeb, K-H., Olafsson, G.

In this note we continue our investigations of the representation theoretic aspects of reflection positivity, also called Osterwalder--Schrader positivity. We explain how this concept relates to affine isometric actions on real Hilbert spaces and how

Externí odkaz: http://arxiv.org/abs/1601.06668

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Weak Poisson structures on infinite dimensional manifolds and hamiltonian actions

Autor: Neeb, K. -H., Sahlmann, H., Thiemann, T.

We introduce a notion of a weak Poisson structure on a manifold $M$ modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra $\cA \subeq C^\infty(M)$ which has to satisfy a non-degeneracy condition (the differen

Externí odkaz: http://arxiv.org/abs/1402.6818

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Pro-Lie groups which are infinite-dimensional Lie groups

Autor: Hofmann, K. H., Neeb, K. -H.

A pro-Lie group is a projective limit of a family of finite-dimensional Lie groups. In this note we show that a pro-Lie group $G$ is a Lie group in the sense that its topology is compatible with a smooth manifold structure for which the group operati

Externí odkaz: http://arxiv.org/abs/math/0609684

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Extensions of Algebraic Groups

Autor: Kumar, S., Neeb, K. -H.

Let $G$ be a connected complex algebraic group and $A$ a connected abelian algebraic group endowed with an algebraic action of $G$ by group automorphisms. In the present note we describe the abelian group $\Ext_{alg}(G,A)$ of algebraic group extensio

Externí odkaz: http://arxiv.org/abs/math/0402453

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