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Associative homotopy Lie algebras and Wronskians

Abstract

We analyze representations of Schlessinger-Stasheff associative homotopy Lie algebras by higher-order differential operators. W-transformations of chiral embeddings of a complex curve related with the Toda equations into Kähler manifolds are shown to be endowed with the homotopy Lie-algebra structures. Extensions of the Wronskian determinants preserving Schlessinger-Stasheff algebras are constructed for the case of n ≥ 1 independent variables.

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Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 11, No. 1, Geometry, 2005.

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Kiselev, A.V. Associative homotopy Lie algebras and Wronskians. J Math Sci 141, 1016–1030 (2007). https://doi.org/10.1007/s10958-007-0028-2

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Keywords

  • Associative Algebra
  • Jacobi Identity
  • Ahler Manifold
  • Conformal Weight
  • Hochschild Cohomology