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Documents  Stolin, Alexander | enregistrements trouvés : 9

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Research talks;Algebra;Algebraic and Complex Geometry;Mathematical Physics

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.

81R10 ; 81R60 ; 16T05

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- 384 p.
ISBN 978-0-8218-3718-4

Contemporary mathematics , 0391

Localisation : Collection 1er étage

géométrie différentielle non commutative # représentation de groupe # physique mathématique # module # théorie de la représentation # algèbre de Lie # algèbre de Jordan # catégorie monoïdale # déformation des structures analytiques # théorie quantique

17-06 ; 81-06 ; 16Dxx ; 16Gxx ; 16W30 ; 17Bxx ; 17Cxx ; 18D10 ; 32Gxx ; 53D55 ; 81Rxx ; 81Txx

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- xviii; 684 p.
ISBN 978-3-642-55360-8

Springer proceedings in mathematics & statistics , 0085

Localisation : Colloque 1er étage (MULH)

déformation # quantification # algèbre de Hom # structure algébrique # algèbre de Hopf # algèbre quantique # système intégrable # théorie des jets # théorie de Lie # algèbre de Lie non commutative # physique mathématique # algèbre ternaire

17-06 ; 16-06 ; 81-06 ; 17Axx ; 17Bxx ; 81Rxx

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- 288 p.
ISBN 978-83-86806-11-9

Banach center publications , 0093

Localisation : Salle des périodiques 1er étage

géométrie différentielle # anneau associatif # anneau non associatif # théorie quantique

53-06 ; 16-06 ; 17-06 ; 81-06 ; 00B25

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Research talks;Algebra;Algebraic and Complex Geometry;Mathematical Physics

We introduce the concept of N-differential graded algebras ($N$-dga), and study the moduli space of deformations of the differential of a $N$-dga. We prove that it is controlled by what we call the $N$-Maurer-Cartan equation. We provide geometric examples such as the algebra of differential forms of depth $N$ on an affine manifold, and $N$-flat covariant derivatives. We also consider deformations of the differential of a $q$-differential graded algebra. We prove that it is controlled by a generalized Maurer-Cartan equation. We find explicit formulae for the coefficients involved in that equation. Deformations of the $3$-differential of $3$-differential graded algebras are controlled by the $(3,N)$ Maurer-Cartan equation. We find explicit formulae for the coefficients appearing in that equation, introduce new geometric examples of $N$-differential graded algebras, and use these results to study $N$-Lie algebroids. We study higher depth algebras, and work towards the construction of the concept of $A^N_ \infty$-algebras. We introduce the concept of N-differential graded algebras ($N$-dga), and study the moduli space of deformations of the differential of a $N$-dga. We prove that it is controlled by what we call the $N$-Maurer-Cartan equation. We provide geometric examples such as the algebra of differential forms of depth $N$ on an affine manifold, and $N$-flat covariant derivatives. We also consider deformations of the differential of a $q$-differential graded ...

16E45 ; 53B50 ; 81R10 ; 16S80 ; 58B32

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Research talks;Algebra;Topology

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 ...

53D55 ; 22Exx ; 81R60 ; 17A32

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Research talks;Algebra

Let $(H, R)$ be a finite dimensional quasitriangular Hopf algebra over a field $k$, and $_H\mathcal{M}$ the representation category of $H$. In this paper, we study the braided autoequivalences of the Drinfeld center $_H^H\mathcal{Y}\mathcal{D}$ trivializable on $_H\mathcal{M}$. We establish a group isomorphism between the group of those autoequivalences and the group of quantum commutative bi-Galois objects of the transmutation braided Hopf algebra $_RH$. We then apply this isomorphism to obtain a categorical interpretation of the exact sequence of the equivariant Brauer group $BM(k, H, R)$ established by Zhang. To this end, we have to develop the braided bi-Galois theory initiated by Schauenburg, which generalizes the Hopf bi-Galois theory over usual Hopf algebras to the one over braided Hopf algebras in a braided monoidal category. Let $(H, R)$ be a finite dimensional quasitriangular Hopf algebra over a field $k$, and $_H\mathcal{M}$ the representation category of $H$. In this paper, we study the braided autoequivalences of the Drinfeld center $_H^H\mathcal{Y}\mathcal{D}$ trivializable on $_H\mathcal{M}$. We establish a group isomorphism between the group of those autoequivalences and the group of quantum commutative bi-Galois objects of the transmutation braided Hopf ...

16T05 ; 16K50

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Research talks;Algebra

The Nakayama automorphism of an Artin-Schelter regular algebra $A$ controls the class of quantum groups that act on the algebra $A$. Several applications are given.

16T05 ; 81R50

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- xvii; 305 p.
ISBN 978-3-540-85331-2

Localisation : Ouvrage RdC (GENE)

groupe topologique # anneau non-associatif # application à la physique

22-06 ; 17-06 ; 81-06 ; 00B15

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