On the associative homotopy Lie algebras and the Wronskians

Details On the associative homotopy Lie algebras and the Wronskians On the associative homotopy Lie algebras and the Wronskians

2004-10-06

arxiv.org/abs/math/0410185v1

Fundam. Appl. Math. 11 (2005) n.1, 159-180.

Mathematics

Rings and Algebras

18 pages, no figures. To appear in: Fundamental'naya i Prikladnaya Matematika (English transl.: Journal of Mathematical Scienc

Scientific paper

Representations of the Schlessinger-Stasheff's associative homotopy Lie algebras in the spaces of higher-order differential operators are analyzed; in particular, a remarkable identity for the Wronskian determinants is obtained. The W-transformations of chiral embeddings, related with the Toda equations, of complex curves into the Kaehler manifolds are shown to be endowed with the homotopy Lie algebra structures. Extensions of the Wronskian determinants that preserve the properties of the Schlessinger-Stasheff's algebras are constructed for the case of $n\geq1$ independent variables.

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