By Abdenacer Makhlouf, Eugen Paal, Sergei D. Silvestrov, Alexander Stolin
This ebook collects the court cases of the Algebra, Geometry and Mathematical Physics convention, held on the college 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 e-book covers deformation thought and quantization; Hom-algebras and n-ary algebraic constructions; Hopf algebra, integrable structures and similar math buildings; jet concept and Weil bundles; Lie idea and functions; non-commutative and Lie algebra and more.
The papers discover the interaction among learn in modern arithmetic and physics excited about generalizations of the most constructions of Lie conception geared 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 e-book merits a large viewers of researchers and complex students.
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Additional resources for Algebra, Geometry and Mathematical Physics: AGMP, Mulhouse, France, October 2011
14, pp. 171–199. Clay Mathematics Institute (2010) 21. : Lie prealgebras. In: Connes, A. et al. ), Noncommutative Geometry and Global Analysis, Contemporary Mathematics, vol. 546, pp. 115–135. American Mathematical Society (2011) 22. : PWB-deformations of N -Koszul algebras. J. Algebra 302, 116–155 (2006) 23. : Calabi-Yau algebras. AG/0612139 24. : Algebraic aspects of the quantum Yang-Baxter equation. Algebra i Analiz (Transl. in Leningrad Math. J. 2 801–828 (1991)), 2, 119–148 (1990) 25. : Higher Koszul algebras and A-infinity algebras.
Karolinsky et al. is known as the classical Kostant’s problem, see [6, 7, 12, 15, 16]. The complete answer to it is still unknown even in the q = 1 case. However, there are examples of α for which the action map U (g) ⊕ End L(α) fin is not surjective. Such examples exist even in the case g is of type A . The main idea of our approach to Kostant’s problem, both in the Lie-algebraic and quantum group cases, is that End L(α) fin has two other presentations. First, it follows from the results of  that End L(α) fin is canonically isomorphic to HomU L(α), L(α) ≥ F , where U is U (g) (resp.
Dubois-Violette 16. : Yang-Mills and some related algebras. In: Rigorous Quantum Field Theory, Progress in Mathematics, vol. 251, pp. 65–78. Birkhaüser (2007) 17. : Noncommutative finite-dimensional manifolds. II. Moduli space and structure of noncommutative 3-spheres. Commun. Math. Phys. 281(1), 23–127 (2008) 18. : Graded algebras and multilinear forms. C. R. Acad. Sci. Paris Ser. I 341, 719–724 (2005) 19. : Multilinear forms and graded algebras. J. Algebra 317, 198–225 (2007) 20. : Noncommutative coordinate algebras.