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# Documents  81R60 | enregistrements trouvés : 4

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## Post-edited  The Weil algebra of a Hopf algebra Dubois-Violette, Michel (Auteur de la Conférence) | CIRM (Editeur )

We give a summary of a joint work with Giovanni Landi (Trieste University) on a non commutative generalization of Henri Cartan's theory of operations, algebraic connections and Weil algebra.

## Multi angle  Deformation quantization of Leibniz algebras Wagemann, Friedrich (Auteur de la Conférence) | CIRM (Editeur )

Let $\mathfrak{h}$ be a finite dimensional real Leibniz algebra. Exactly as the linear dual space of a Lie algebra is a Poisson manifold with respect to the Kostant-Kirillov-Souriau (KKS) bracket, $\mathfrak{h}^*$ can be viewed as a generalized Poisson manifold. The corresponding bracket is roughly speaking the evaluation of the KKS bracket at $0$ in one variable. This (perhaps strange looking) bracket comes up naturally when quantizing $\mathfrak{h}^*$ in an analoguous way as one quantizes the dual of a Lie algebra. Namely, the product $X \vartriangleleft Y = exp(ad_X)(Y)$ can be lifted to cotangent level and gives than a symplectic micromorphism which can be quantized by Fourier integral operators. This is joint work with Benoit Dherin (2013). More recently, we developed with Charles Alexandre, Martin Bordemann and Salim Rivire a purely algebraic framework which gives the same star-product. Let $\mathfrak{h}$ be a finite dimensional real Leibniz algebra. Exactly as the linear dual space of a Lie algebra is a Poisson manifold with respect to the Kostant-Kirillov-Souriau (KKS) bracket, $\mathfrak{h}^*$ can be viewed as a generalized Poisson manifold. The corresponding bracket is roughly speaking the evaluation of the KKS bracket at $0$ in one variable. This (perhaps strange looking) bracket comes up naturally when quantizing ...

## Multi angle  Quanta of geometry Connes, Alain (Auteur de la Conférence) | CIRM (Editeur )

J'exposerai les résultats très récents obtenus en collaboration avec Chamseddine et Suijlekom sur l'unification des constantes de couplage dans l'approche de la physique par la géométrie noncommutative.

## Multi angle  Twisted equivariant $\mathrm{K}$-theory and topological phases Kubota, Yosuke (Auteur de la Conférence) | CIRM (Editeur )

The classification of topological phases in each Altland-Zirnbauer symmetry class is related to one of 2 complex or 8 real $\mathrm{K}$-theory by Kitaev. A more general framework, in which we deal with systems with an arbitrary symmetry of quantum mechanics specified by Wigner's theorem, is introduced by Freed and Moore by using a generalization of twisted $\mathrm{K}$-theory. In this talk, we introduce the definition of twisted $\mathrm{K}$-theory in the sense of Freed-Moore for $C^*$-algebras, which gives a framework for the study of topological phases of non-periodic systems with a symmetry of quantum mechanics. Moreover, we introduce uses of basic tools in $\mathrm{K}$-theory of operator algebras such as inductions and the Green-Julg isomorphism for the study of topological phases. The classification of topological phases in each Altland-Zirnbauer symmetry class is related to one of 2 complex or 8 real $\mathrm{K}$-theory by Kitaev. A more general framework, in which we deal with systems with an arbitrary symmetry of quantum mechanics specified by Wigner's theorem, is introduced by Freed and Moore by using a generalization of twisted $\mathrm{K}$-theory. In this talk, we introduce the definition of twisted \$\mathr...

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