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L’hyperanneau des classes d’adèles

Alain Connes (2011)

Journal de Théorie des Nombres de Bordeaux

J’exposerai ici quelques résultats récents (obtenus en collaboration avec C. Consani [3], [4], [5], [6]) qui portent sur le cas limite de la “caractéristique 1 ”. Le but principal est de montrer que l’espace des classes d’adèles d’un corps global, qui jusqu’à présent n’a été considéré que comme un espace (non-commutatif), admet en fait une structure algébrique naturelle. Nous verrons également que la construction de l’anneau de Witt d’un anneau de caractéristique p > 1 admet un analogue en caractéristique...

Lie groupoids of mappings taking values in a Lie groupoid

Habib Amiri, Helge Glöckner, Alexander Schmeding (2020)

Archivum Mathematicum

Endowing differentiable functions from a compact manifold to a Lie group with the pointwise group operations one obtains the so-called current groups and, as a special case, loop groups. These are prime examples of infinite-dimensional Lie groups modelled on locally convex spaces. In the present paper, we generalise this construction and show that differentiable mappings on a compact manifold (possibly with boundary) with values in a Lie groupoid form infinite-dimensional Lie groupoids which we...

Lie triple ideals and Lie triple epimorphisms on Jordan and Jordan-Banach algebras

M. Brešar, M. Cabrera, M. Fošner, A. R. Villena (2005)

Studia Mathematica

A linear subspace M of a Jordan algebra J is said to be a Lie triple ideal of J if [M,J,J] ⊆ M, where [·,·,·] denotes the associator. We show that every Lie triple ideal M of a nondegenerate Jordan algebra J is either contained in the center of J or contains the nonzero Lie triple ideal [U,J,J], where U is the ideal of J generated by [M,M,M]. Let H be a Jordan algebra, let J be a prime nondegenerate Jordan algebra with extended centroid C and unital central closure Ĵ, and let...

Limit laws for products of free and independent random variables

Hari Bercovici, Vittorino Pata (2000)

Studia Mathematica

We determine the distributional behavior of products of free (in the sense of Voiculescu) identically distributed random variables. Analogies and differences with the classical theory of independent random variables are then discussed.

Limit Measures Related to the Conditionally Free Convolution

Melanie Hinz, Wojciech Młotkowski (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

We describe the limit measures for some class of deformations of the free convolution, introduced by A. D. Krystek and Ł. J. Wojakowski. In particular, we provide a counterexample to a conjecture from their paper.

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