Algebra, Geometry and Mathematical Physics: Agmp, Mulhouse, France, October 2011

ISBN-13: 9783642553608 / Angielski / Twarda / 2014 / 684 str.

Abdenacer Makhlouf; Eugen Paal; Sergei Silvestrov

Opis

This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more.The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond.The book benefits a broad audience of researchers and advanced students.

Spis treści

Part I Algebra: Poincaré duality for Koszul algebras: M.Dubois-Violette.- Poincaré duality for Koszul algebras: M. Dubois-Violette.- Quantized reduced fusion elements and Kostant’s problem: E. Karolinsky et al.- Commutants and centers in a 6-parameter family of quadratically linked quantum plane algebras: F. Ekström et al.- Burchnall-Chaundy theory for Ore extensions: J. Richter.- Homotopy commutative algebra and 2-nilpotent Lie algebra: M. Dubois-Violette et al.- Subalgebra depths within the path algebra of an acyclic quiver: L. Kadison et al.- Lie algebras with given properties of subalgebras and elements: P. Zusmanovich.- Construction of symplectic quadratic Lie algebras from Poisson algebras: S. Benayadi.- Structure and Cohomology of 3-Lie Algebras Induced by Lie Algebras: J. Arnlind et al.- A review of Peirce decomposition for unitary (−1,−1)-Freudenthal Kantor triple systems: N. Kamiya et al.- Universal Algebra Applied to Hom-Associative Algebras and More: L. Hellström et al.- Constructions of Quadratic n-ary Hom-Nambu algebras: F. Ammar et al.- A comparison of Leibniz and Lie cohomology and deformations: A. Fialowski.- Rigid current Lie algebras: E. Remm et al.- Deformations of Diagrams: A. Siqveland.- Noncommutative Algebraic Varieties: A. Siqveland.- Computing noncommutative deformations: E. Eriksen.- Geometric Classification of 4-Dimensional Superalgebras: A. Armour et al.- Distributivity in Quandles and Quasigroups: M. Elhamdadi.- Part II Geometry: Torsors and ternaryMoufang loops arising in projective geometry: W. Bertram.-  Graded q-differential polynomial algebra of connection form: V. Abramov et al.- Double category related to path space parallel transport and representations of Lie 2 groups: S. Chatterjee et al.- A note on jet and geometric approach to higher order connections: M. Rahula et al.- Classification of principal connections on]W 2PE: J. Vondra.- The generic rank of A–planar structures: J. Hrdina.- Geometric Approach to Ghost Fields: V. Abramov et al.- On Sinyukov’s equations in their relation to a curvature operator of second kind: I. Hinterleitner et al.- On dimensions of vector spaces of conformal Killing forms: S. E. Stepanov.- Part III Dynamical Symmetries and Conservation Laws: Causality from dynamical symmetry: an example from local scale-invariance: M. Henkel.- Reaction-diffusion systems with constant diffusivities: conditional symmetries and form-preserving transformations: C. Roman et al.- Solution to the inverse problem of reconstructing permittivity of an n-sectional diaphragm in a rectangular waveguide: Yu. G. Smirnov et al.- Some conservation laws for a class of Hamilton-Jacobi-Bellman equations: M.L. Gandarias et al.- Self-adjointness and conservation laws for a Generalized Dullin-Gottwald-Holm equation: M. S. Bruzón et al.- Semi analytical Solutions of a Heat-Mass Transfer Problem via Group Theoretic Approach: M.B. Abd-el-Malek et al.- Part IV Mathematical Physics and Applications: Realizations of Affine Lie Algebra A(1) 1 at Negative Levels: J. Dong et al.- Invariance and symmetries of cubic and ternary algebras: R. Kerner.- Calculation of Decay Times for Simple Modules: O. Gravir Imenes.- On the Detection of Permutation Polynomials: M. Gharibah.- Scalar-tensor and multiscalar-tensor gravity and cosmological models: P. Kuusk et al.- Index.