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Characterizing Algebraic Invariants by Differential Radical Invariants ⋆
"... Abstract We prove that any invariant algebraic set of a given polynomial vector field can be algebraically represented by one polynomial and a finite set of its successive Lie derivatives. This socalled differential radical characterization relies on a sound abstraction of the reachable set of solu ..."
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Cited by 4 (2 self)
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Abstract We prove that any invariant algebraic set of a given polynomial vector field can be algebraically represented by one polynomial and a finite set of its successive Lie derivatives. This socalled differential radical characterization relies on a sound abstraction of the reachable set
Symplectic reflection algebras, CalogeroMoser space, and deformed HarishChandra homomorphism
 Invent. Math
"... To any finite group Γ ⊂ Sp(V) of automorphisms of a symplectic vector space V we associate a new multiparameter deformation, Hκ, of the algebra C[V]#Γ, smash product of Γ with the polynomial algebra on V. The parameter κ runs over points of CP r, where r = number of conjugacy classes of symplectic ..."
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Cited by 280 (39 self)
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‘rational ’ degenerations of the double affine Hecke algebra introduced earlier by Cherednik. Let Γ = Sn, the Weyl group of g = gl n. We construct a 1parameter deformation of the HarishChandra homomorphism from D(g) g, the algebra of invariant polynomial differential operators on the Lie algebra g = gl n
Algebraic and Differential Invariants
 FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, BUDAPEST 2011, LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES (403)
, 2011
"... This article highlights a coherent series of algorithmic tools to compute and work with algebraic and differential invariants. ..."
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Cited by 5 (5 self)
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This article highlights a coherent series of algorithmic tools to compute and work with algebraic and differential invariants.
Differential Invariant Algebras
"... Abstract. The equivariant method of moving frames provides an algorithmic procedure for determining and analyzing the structure of algebras of differential invariants for both finitedimensional Lie groups and infinitedimensional Lie pseudogroups. This paper surveys recent developments, including ..."
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Cited by 3 (1 self)
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Abstract. The equivariant method of moving frames provides an algorithmic procedure for determining and analyzing the structure of algebras of differential invariants for both finitedimensional Lie groups and infinitedimensional Lie pseudogroups. This paper surveys recent developments, including
Algebraic and rational differential invariants
"... These notes start with an introduction to differential invariants. They continue with an algebraic treatment of the theory. The algebraic, differential algebraic and differential geometric tools that are necessary to the development of the theory are explained in detail. We expose the recent result ..."
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These notes start with an introduction to differential invariants. They continue with an algebraic treatment of the theory. The algebraic, differential algebraic and differential geometric tools that are necessary to the development of the theory are explained in detail. We expose the recent
Cherednik algebras and differential operators on quasiinvariants
 Duke Math. J
"... We develop representation theory of the rational Cherednik algebra Hc associated to a finite Coxeter group W in a vector space h, and a parameter “c. ” We use it to show that, for integral values of “c, ” the algebra Hc is simple and Morita equivalent to D(h)#W, the cross product of W with the algeb ..."
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Cited by 67 (12 self)
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with the algebra of polynomial differential operators on h. O. Chalykh, M. Feigin, and A. Veselov [CV1], [FV] introduced an algebra, Qc, of quasiinvariant polynomials on h, such that C[h] W ⊂ Qc ⊂ C[h]. We prove that the algebra D(Qc) of differential operators on quasiinvariants is a simple algebra, Morita
Invariance of Conjunctions of Polynomial Equalities for Algebraic Differential Equations?
"... Abstract In this paper we seek to provide greater automation for formal deductive verification tools working with continuous and hybrid dynamical systems. We present an efficient procedure to check invariance of conjunctions of polynomial equalities under the flow of polynomial ordinary differenti ..."
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differential equations. The procedure is based on a necessary and sufficient condition that characterizes invariant conjunctions of polynomial equalities. We contrast this approach to an alternative one which combines fast and sufficient (but not necessary) conditions using differential cuts for soundly
Algebraic Property Testing: The Role of Invariance
, 2007
"... We argue that the symmetries of a property being tested play a central role in property testing. We support this assertion in the context of algebraic functions, by examining properties of functions mapping a vector space K n over a field K to a subfield F. We consider Flinear properties that are i ..."
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Cited by 51 (16 self)
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that are invariant under linear transformations of the domain and prove that an O(1)local “characterization ” is a necessary and sufficient condition for O(1)local testability when K  = O(1). (A local characterization of a property is a definition of a property in terms of local constraints satisfied
Constructive Algebra for Differential Invariants Contents
, 2008
"... Constructive Algebra for Differential Invariants Differential invariants arise in equivalence problems and are used in symmetry reduction techniques ..."
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Constructive Algebra for Differential Invariants Differential invariants arise in equivalence problems and are used in symmetry reduction techniques
Differential invariants and curved BernsteinGelfandGelfand sequences
 JOUR. REINE ANGEW. MATH
, 2000
"... We give a simple construction of the BernsteinGelfandGelfand sequences of natural differential operators on a manifold equipped with a parabolic geometry. This method permits us to define the additional structure of a bilinear differential “cup product ” on this sequence, satisfying a Leibniz ru ..."
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Cited by 78 (6 self)
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rule up to curvature terms. It is not associative, but is part of an A∞algebra of multilinear differential operators, which we also obtain explicitly. We illustrate the construction in the case of conformal differential geometry, where the cup product provides a widereaching generalization
Results 1  10
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