Algebra, Geometry and Mathematical Physics: AGMP, Mulhouse, by Abdenacer Makhlouf, Eugen Paal, Sergei D. Silvestrov,

By Abdenacer Makhlouf, Eugen Paal, Sergei D. Silvestrov, Alexander Stolin

This e-book collects the lawsuits of the Algebra, Geometry and Mathematical Physics convention, held on the collage of Haute Alsace, France, October 2011. geared up within the 4 parts of algebra, geometry, dynamical symmetries and conservation legislation and mathematical physics and purposes, the booklet covers deformation concept and quantization; Hom-algebras and n-ary algebraic constructions; Hopf algebra, integrable platforms and comparable math constructions; jet conception and Weil bundles; Lie idea and functions; non-commutative and Lie algebra and more.

The papers discover the interaction among study in modern arithmetic and physics all in favour of generalizations of the most buildings of Lie conception aimed toward quantization and discrete and non-commutative extensions of differential calculus and geometry, non-associative constructions, activities of teams and semi-groups, non-commutative dynamics, non-commutative geometry and purposes in physics and beyond.

The booklet merits a large viewers of researchers and complicated students.

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Additional resources for Algebra, Geometry and Mathematical Physics: AGMP, Mulhouse, France, October 2011

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This paper is organized as follows. In Sect. 2 we recall the definition of the version of quantized universal enveloping algebra used in this paper, and some related constructions that will be useful in the sequel. In Sect. 3 we construct an isomorphism Quantized Reduced Fusion Elements and Kostant’s Problem 29 F[0] K α + K α and, as a corollary, provide a construction HomU L(α), L(α) ≥ F of a star-product on F[0] K α + K α in terms of the Shapovalov form on L(α). In Sect. 4 we study limiting properties of fusion elements and the corresponding star-products.

Was supported in part by the Royal Swedish Academy of Sciences, A. —by the Crafoord Prize research grant, V. –by NSF grant DMS-0901616. 36 E. Karolinsky et al. References 1. : Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of the classical Yang-Baxter equations. Sov. Math. Dokl. 27, 68–71 (1983) 2. : On Poisson homogeneous spaces of Poisson-Lie groups. Theor. Math. Phys. 95, 524–525 (1993) 3. : Quantization of coboundary Lie bialgebras. Ann. Math. 2(171), 1267–1345 (2010) 4.

Karolinsky et al. References 1. : Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of the classical Yang-Baxter equations. Sov. Math. Dokl. 27, 68–71 (1983) 2. : On Poisson homogeneous spaces of Poisson-Lie groups. Theor. Math. Phys. 95, 524–525 (1993) 3. : Quantization of coboundary Lie bialgebras. Ann. Math. 2(171), 1267–1345 (2010) 4. : Lectures on the dynamical Yang-Baxter equations. In: Quantum groups and Lie theory (Durham, 1999), pp. 89–129. London Mathematical Society Lecture Note Series, 290.

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