1,824 research outputs found
Dirac-Jacobi Bundles
We show that a suitable notion of Dirac-Jacobi structure on a generic line
bundle , is provided by Dirac structures in the omni-Lie algebroid of .
Dirac-Jacobi structures on line bundles generalize Wade's -Dirac structures and unify generic (i.e.~non-necessarily coorientable)
precontact distributions, Dirac structures and local Lie algebras with one
dimensional fibers in the sense of Kirillov (in particular, Jacobi structures
in the sense of Lichnerowicz). We study the main properties of Dirac-Jacobi
structures and prove that integrable Dirac-Jacobi structures on line-bundles
integrate to (non-necessarily coorientable) precontact groupoids. This puts in
a conceptual framework several results already available in literature for
-Dirac structures.Comment: v6: 55 pages, corrected some minor mistakes, final version, to appear
in J. Sympl. Geom, 16 (2018
A criterion for existence of right-induced model structures
Suppose that is a functor whose target is a
Quillen model category. We give a succinct sufficient condition for the
existence of the right-induced model category structure on in the
case when admits both adjoints. We give several examples, including
change-of-rings, operad-like structures, and anti-involutive structures on
infinity categories. For the last of these, we explore anti-involutive
structures for several different models of -categories, and show
that known Quillen equivalences between base model categories lift to
equivalences
Holomorphic geometric models for representations of -algebras
Representations of -algebras are realized on section spaces of
holomorphic homogeneous vector bundles. The corresponding section spaces are
investigated by means of a new notion of reproducing kernel, suitable for
dealing with involutive diffeomorphisms defined on the base spaces of the
bundles. Applications of this technique to dilation theory of completely
positive maps are explored and the critical role of complexified homogeneous
spaces in connection with the Stinespring dilations is pointed out. The general
results are further illustrated by a discussion of several specific topics,
including similarity orbits of representations of amenable Banach algebras,
similarity orbits of conditional expectations, geometric models of
representations of Cuntz algebras, the relationship to endomorphisms of
, and non-commutative stochastic analysis.Comment: 45 page
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