Algebra, Geometry and Mathematical Physics: AGMP, Mulhouse, France, October 2011 (Springer Proceedings in Mathematics & Statistics Book 85)

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. Part I Algebra -- Part Ii Geometry -- Part Iii Dynamical Symmetries And Conservation Laws -- Part Iv Mathematical Physics And Applications. Edited By Abdenacer Makhlouf, Eugen Paal, Sergei D. Silvestrov, Alexander Stolin. Front Matter....Pages i-xviii Front Matter....Pages 1-1 Poincaré Duality for Koszul Algebras....Pages 3-26 Quantized Reduced Fusion Elements and Kostant’s Problem....Pages 27-36 Commutants and Centers in a 6-Parameter Family of Quadratically Linked Quantum Plane Algebras....Pages 37-59 Burchnall-Chaundy Theory for Ore Extensions....Pages 61-70 Homotopy Commutative Algebra and 2-Nilpotent Lie Algebra....Pages 71-81 Subalgebra Depths Within the Path Algebra of an Acyclic Quiver....Pages 83-97 Lie Algebras with Given Properties of Subalgebras and Elements....Pages 99-109 Construction of Symplectic Quadratic Lie Algebras from Poisson Algebras....Pages 111-122 Structure and Cohomology of 3-Lie Algebras Induced by Lie Algebras....Pages 123-144 A Review of Peirce Decomposition for Unitary $$(-1,-1)$$ -Freudenthal Kantor Triple Systems....Pages 145-155 Universal Algebra Applied to Hom-Associative Algebras, and More....Pages 157-199 Constructions of Quadratic $$n$$ -ary Hom-Nambu Algebras....Pages 201-232 A Comparison of Leibniz and Lie Cohomology and Deformations....Pages 233-246 Rigid Current Lie Algebras....Pages 247-258 Deformations of Diagrams....Pages 259-274 Noncommutative Algebraic Varieties....Pages 275-283 Computing Noncommutative Deformations....Pages 285-290 Geometric Classification of 4-Dimensional Superalgebras....Pages 291-323 Distributivity in Quandles and Quasigroups....Pages 325-340 Front Matter....Pages 341-341 Torsors and Ternary Moufang Loops Arising in Projective Geometry....Pages 343-360 Front Matter....Pages 341-341 Graded $$q$$ -Differential Polynomial Algebra of Connection Form....Pages 361-377 Double Category Related to Path Space Parallel Transport and Representations of Lie 2 Groups....Pages 379-391 Differential Geometry of Microlinear Frölicher Spaces IV-1....Pages 393-443 A Note on Jet and Geometric Approach to Higher Order Connections....Pages 445-455 Classification of Principal Connections on $${\widetilde{W}}^2PE$$ ....Pages 457-466 The Generic Rank of A -Planar Structures....Pages 467-473 Geometric Approach to Ghost Fields....Pages 475-488 On Sinyukov’s Equations in Their Relation to a Curvature Operator of Second Kind....Pages 489-494 On Dimensions of Vector Spaces of Conformal Killing Forms....Pages 495-507 Front Matter....Pages 509-509 Causality from Dynamical Symmetry: An Example from Local Scale-Invariance....Pages 511-531 Reaction-Diffusion Systems with Constant Diffusivities: Conditional Symmetries and Form-Preserving Transformations....Pages 533-553 Solution to the Inverse Problem of Reconstructing Permittivity of an $$n$$ -Sectional Diaphragm in a Rectangular Waveguide....Pages 555-566 Some Conservation Laws for a Class of Hamilton-Jacobi-Bellman Equations....Pages 567-576 Self-Adjointness and Conservation Laws for a Generalized Dullin-Gottwald-Holm Equation....Pages 577-586 Semi Analytical Solutions of a Heat-Mass Transfer Problem Via Group Theoretic Approach....Pages 587-600 Front Matter....Pages 601-601 Realizations of Affine Lie Algebra $${A^{(1)}_1}$$ at Negative Levels....Pages 603-616 Invariance and Symmetries of Cubic and Ternary Algebras....Pages 617-637 Calculation of Decay Times for Simple Modules....Pages 639-650 On the Detection of Permutation Polynomials....Pages 651-660 Scalar-Tensor and Multiscalar-Tensor Gravity and Cosmological Models....Pages 661-672 Front Matter....Pages 601-601 The Other Half of Quantum Geometry: A First Glimpse....Pages 673-679 Back Matter....Pages 681-684