By Abdenacer Makhlouf, Eugen Paal, Sergei D. Silvestrov, Alexander Stolin
This booklet collects the complaints 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 publication covers deformation conception and quantization; Hom-algebras and n-ary algebraic buildings; Hopf algebra, integrable structures and similar math constructions; jet conception and Weil bundles; Lie thought and functions; non-commutative and Lie algebra and more.
The papers discover the interaction among study in modern arithmetic and physics fascinated about generalizations of the most buildings of Lie thought aimed toward quantization and discrete and non-commutative extensions of differential calculus and geometry, non-associative buildings, activities of teams and semi-groups, non-commutative dynamics, non-commutative geometry and purposes in physics and beyond.
The ebook advantages a vast viewers of researchers and complicated students.
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Extra info for Algebra, Geometry and Mathematical Physics: AGMP, Mulhouse, France, October 2011
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Finding in a systematic way bases for the algebras for various choices of parameters becomes an elaborate task requiring non-trivial use of the Bergman’s diamond lemma and relations (1) as well as some symmetries of the relations and their consequences for case reductions of various subtle parameter subsets. It appears in the course of this analysis, that the basis takes a somewhat simpler form for a large subset of parameters given by a system of certain inequalities. This set of “generic” parameters, as we call it, and the bases yield useful grading structures, used in Sect.
Categorification of Wedderburn’s basis for C[Sn ]. Arch. Math. 91, 1–11 (2008) 18. : Quantum conjugacy classes of simple matrix groups. Comm. Math. Phys. 272, 635–660 (2007) Commutants and Centers in a 6-Parameter Family of Quadratically Linked Quantum Plane Algebras Fredrik Ekström and Sergei D. Silvestrov Abstract We consider a family of associative algebras, defined as the quotient of a free algebra with the ideal generated by a set of multi-parameter deformed commutation relations between four generators consisting of five quantum plane relations between pairs of generators and one sub-quadratic relation inter-linking all four generators.