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Documents  58B32 | enregistrements trouvés : 6

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- 348 p.

Banach center publications , 0061

Localisation : Salle des périodiques 1er étage

analyse globale # théorie quantique # géométrie des groupes quantiques # groupe quantique # géométrie non-commutative # algèbre de Hopf # cohomologie cyclique # cohomologie d'Hochschild # extension de Galois # opérateur de Dirac # foliation # géométrie de Poisson # C*-algèbre # tresse # calcul différentiel # localisation # K-theorie

81-06 ; 58-06 ; 58B32 ; 81R50

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Research talks

Skein algebras are certain diagrammatically defined algebras spanned by tangles drawn on the cylinder of a surface, with multiplication given by stacking diagrams. Quantum cluster algebras are certain systems of mutually birational quantum tori whose defining relations are encoded in a quiver drawn on the surface. The category of quantum character sheaves is a $q$-deformation of the category of ad-equivariant $D$-modules on the group $G$, expressed through an algebra $D_q (G)$ of “q-difference” operators on $G$.
In this I talk I will explain that these are in fact three sides of the same coin - namely they each arise as different flavors of factorization homology, and hence fit in the framework of four-dimensional topological field theory.
Skein algebras are certain diagrammatically defined algebras spanned by tangles drawn on the cylinder of a surface, with multiplication given by stacking diagrams. Quantum cluster algebras are certain systems of mutually birational quantum tori whose defining relations are encoded in a quiver drawn on the surface. The category of quantum character sheaves is a $q$-deformation of the category of ad-equivariant $D$-modules on the group $G$, ...

13F60 ; 16TXX ; 17B37 ; 58B32

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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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- 169 p.
ISBN 978-0-521-01041-2

London mathematical society lecture note series , 0292

Localisation : Collection 1er étage

groupe quantique # géométrie des groupes quantiques # algèbre de Hopf # géométrie non commutative

17B37 ; 17B05 ; 58B32 ; 81R50

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- 299 p.
ISBN 978-3-540-24406-6

Lecture notes in mathematics , 1865

Localisation : Collection 1er étage

groupe quantique # probabilité non commutative # probabilité quantique # processus de Levy # processus à incrément indépendant # calcul stochastique quantique # algèbre d'opérateur auto-adjoint # dilatation # cocycle # système de produit

60-06 ; 81-06 ; 60G51 ; 81S25 ; 46L60 ; 58B32 ; 47A20 ; 16W30

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- 336 p.
ISBN 978-3-540-24407-3

Lecture notes in mathematics , 1866

Localisation : Collection 1er étage

processus avec incrément indépendant # calcul stochastique quantique # algèbre d'opérateur auto-adjoint # géométrie des groupes quantiques # probabilité quantique # processus de Lévy

60G51 ; 81S25 ; 46L60 ; 58B32 ; 47A20 ; 16W30

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