Deformation Theory of Algebras and Structures and Applications (Nato Science Series C:, 247)

This volume is a result of a meeting which took place in June 1986 at 'll Ciocco" in Italy entitled 'Deformation theory of algebras and structures and applications'. It appears somewhat later than is perhaps desirable for a volume resulting from a summer school. In return it contains a good many results which were not yet available at the time of the meeting. In particular it is now abundantly clear that the Deformation theory of algebras is indeed central to the whole philosophy of deformations/perturbations/stability. This is one of the main results of the 254 page paper below (practically a book in itself) by Gerstenhaber and Shack entitled "Algebraic cohomology and defor­ mation theory". Two of the main philosphical-methodological pillars on which deformation theory rests are the fol­ lowing • (Pure) To study a highly complicated object, it is fruitful to study the ways in which it can arise as a limit of a family of simpler objects: "the unraveling of complicated structures" . • (Applied) If a mathematical model is to be applied to the real world there will usually be such things as coefficients which are imperfectly known. Thus it is important to know how the behaviour of a model changes as it is perturbed (deformed). Front Matter....Pages i-viii The philosophy of deformations: introductory remarks and a guide to this volume....Pages 1-7 Front Matter....Pages 9-9 Algebraic Cohomology and Deformation Theory....Pages 11-264 Perturbations of Lie Algebra Structures....Pages 265-355 Cohomology of Current Lie Algebras....Pages 357-374 An Example of Formal Deformations of Lie Algebras....Pages 375-401 On the Rigidity of Solvable Lie Algebras....Pages 403-445 Triangular Algebras....Pages 447-498 Front Matter....Pages 499-499 Deformation Theory for Algebras of Analytic Functions....Pages 501-535 Close Operator Algebras....Pages 537-556 Perturbations of function algebras....Pages 557-563 Perturbations of Multiplication and Homomorphisms....Pages 565-579 Front Matter....Pages 581-581 Local Isoformal Deformation Theory for Meromorphic Differential Equations Near an Irregular Singularity....Pages 583-700 Geometric and Lie-Theoretic Principles in Pure and Applied Deformation Theory....Pages 701-796 Complexes of Differential Operators and Symmetric Spaces....Pages 797-827 Deformation Theory of Geometric and Algebraic Structures....Pages 829-838 Some Rigidity Results in the Deformation Theory of Symmetric Spaces....Pages 839-851 Front Matter....Pages 853-853 Applications of the Deformations of the Algebraic Structures to Geometry and Mathemetical Physics....Pages 855-896 Formal Deformations of the Poisson Lie Algebra of a Symplectic Manifold and Star-Products. Existence, Equivalence, Derivations....Pages 897-960 Invariant Deformations of the Poisson Lie Algebra of a Symplectic Manifold and Star-Products....Pages 961-972 Front Matter....Pages 973-973 A remarkable matrix....Pages 975-980 Front Matter....Pages 973-973 Deformation Stability of Periodic and Quasi Periodic Motion in Dissipative Systems....Pages 981-1013 Back Matter....Pages 1015-1030 This volume is a result of a meeting which took place in June 1986 at 'll Ciocco" in Italy entitled 'Deformation theory of algebras and structures and applications'. It appears somewhat later than is perhaps desirable for a volume resulting from a summer school. In return it contains a good many results which were not yet available at the time of the meeting. In particular it is now abundantly clear that the Deformation theory of algebras is indeed central to the whole philosophy of deformations/perturbations/stability. This is one of the main results of the 254 page paper below (practically a book in itself) by Gerstenhaber and Shack entitled "Algebraic cohomology and deforƯ mation theory". Two of the main philosophical-methodological pillars on which deformation theory rests are the folƯ lowing " (Pure) To study a highly complicated object, it is fruitful to study the ways in which it can arise as a limit of a family of simpler objects: "the unraveling of complicated structures" ." (Applied) If a mathematical model is to be applied to the real world there will usually be such things as coefficients which are imperfectly known. Thus it is important to know how the behaviour of a model changes as it is perturbed (deformed) Proceedings of the NATO Advanced Study Institute, Il Ciocci, Casterecchio Pascoli, Tuscan, June 1-14, 1986 Edited By Michiel Hazewinkel, Murray Gerstenhaber.