Higher-Dimensional Generalizations of Affine Kac-Moody and Virasoro Conformal Lie Algebras |
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Authors: | M Golenishcheva-Kutuzova |
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Institution: | (1) Department of Mathematics, University of Florida, PO Box 118105, Gainesville, FL 32611-8105, USA |
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Abstract: | We discuss the generalizations of the notion of Conformal Algebra and Local Distribution Lie algebras for multi-dimensional
bases. We replace the algebra of Laurent polynomials on by an infinite-dimensional representation (with some additional structures) of a simple finite-dimensional Lie algebra in the space of regular functions on the corresponding Grassmann variety that can be described as a ``right' higher-dimensional generalization of from the point of view of a corresponding group action. For it gives us the usual Vertex Algebra notion. We construct the higher dimensional generalizations of the Virasoro and the
Affine Kac-Moody Conformal Lie algebras explicitly and in terms of the Operator Product Expansion. |
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