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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Communicated by L. Takhtajan
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Golenishcheva-Kutuzova, M. Higher-Dimensional Generalizations of Affine Kac-Moody and Virasoro Conformal Lie Algebras. Commun. Math. Phys. 263, 583–610 (2006). https://doi.org/10.1007/s00220-005-1502-7
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DOI: https://doi.org/10.1007/s00220-005-1502-7