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A class of graded Lie algebras of vector fields and first order differential operators (1994)

Post, Gerhard

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 35 (1994), S. 6838-6856

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: Finite-dimensional Lie algebras of polynomial vector fields on Rn, that contain the elements ∂/∂xi and xi(∂/∂xi) for i=1...n were studied. To any Lie algebra @FL of this class, an N-valued n×n matrix A and a set of special elements S⊆{1,...,n} are associated. It is proven that the pair (A,S) necessarily satisfies two properties. Conversely, to any pair (A,S) satisfying those two properties is associated a Lie algebra @FL(A,S), such that @FL(A,S) is maximal in the class of all @FL with matrix A and special elements S. For the Lie algebras @FL(A,S) the possible extensions to first order differential operators, and its modules of C∞ functions are discussed. © 1994 American Institute of Physics.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.530645

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