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Invariants of Quadratic Differential Forms
Classic monograph offers a brief account of the invariant theory connected with a single quadratic differential form. Includes historical overview; methods of Christoffel, Lie, Maschke; and geometrical, dynamical methods. 1960 edition.
Invariants of Quadratic Differential Forms
An early tract for students of differential geometry and mathematical physics.
Equivalence, Invariants and Symmetry
Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied mathematics and algebra, this book presents an innovative synthesis of methods used to study problems of equivalence and symmetry which arise in a variety of mathematical fields and physical applications. Systematic and constructive methods for solving equivalence problems and calculating symmetries are developed and applied to a wide variety of mathematical systems, including differential equations, variational problems, manifolds, Riemannian metrics, polynomials and differential operators. Particular emphasis is given to the construction and classification of invariants, and to the reductions of complicated objects to simple canonical forms. This book will be a valuable resource for students and researchers in geometry, analysis, algebra, mathematical physics and other related fields.
Introduction to the Algebraic Theory of Invariants of Differential Equations
Considers polynominal invariants & comitants of autonomous systems of differential equations with right-hand sides relative to various transformation groups of phase space. Contains an in-depth discussion of the two-dimensional system with quadratic right-hand sides. Features numerous applications to the qualitative theory of differential equations.
Differential Invariants of Prehomogeneous Vector Spaces
Differential invariants of prehomogeneous vector spaces studies in detail two differential invariants of a discriminant divisor of a prehomogeneous vector space. The Bernstein-Sato polynomial and the spectrum, which encode the monodromy and Hodge theoretic informations of an associated Gauss-Manin system. The theoretical results are applied to discriminants in the representation spaces of the Dynkin quivers An, Dn, E6, E7 and three non classical series of quiver representations.
Rings of Differential Operators on Classical Rings of Invariants
"September 1989, Volume 81, number 412 (third of 6 numbers)."
Groups, Invariants, Integrals, and Mathematical Physics
This volume presents lectures given at the Wisła 20-21 Winter School and Workshop: Groups, Invariants, Integrals, and Mathematical Physics, organized by the Baltic Institute of Mathematics. The lectures were dedicated to differential invariants – with a focus on Lie groups, pseudogroups, and their orbit spaces – and Poisson structures in algebra and geometry and are included here as lecture notes comprising the first two chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and category theory. Specific topics covered include: The multisymplectic and variational nature of Mo...
A Practical Guide to the Invariant Calculus
This book explains recent results in the theory of moving frames that concern the symbolic manipulation of invariants of Lie group actions. In particular, theorems concerning the calculation of generators of algebras of differential invariants, and the relations they satisfy, are discussed in detail. The author demonstrates how new ideas lead to significant progress in two main applications: the solution of invariant ordinary differential equations and the structure of Euler-Lagrange equations and conservation laws of variational problems. The expository language used here is primarily that of undergraduate calculus rather than differential geometry, making the topic more accessible to a student audience. More sophisticated ideas from differential topology and Lie theory are explained from scratch using illustrative examples and exercises. This book is ideal for graduate students and researchers working in differential equations, symbolic computation, applications of Lie groups and, to a lesser extent, differential geometry.
