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arxiv: math/0410185 · v1 · submitted 2004-10-06 · 🧮 math.RA · math.AC

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On the associative homotopy Lie algebras and the Wronskians

A. V. Kiselev
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classification 🧮 math.RA math.AC
keywords algebrashomotopyassociativedeterminantsschlessinger-stasheffwronskianalgebraanalyzed
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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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  1. The Alternating Compositions of Weighted Differential Operators Yield The Weights' Wronskian With Which Constant?

    math.CO 2026-05 accept novelty 7.0

    Alternating composition of 2p operators w_j(x) ∂_x^p yields const(p) times the Wronskian of the w_j, with const(p) expressed as a signed sum over late-growing permutations and computed explicitly for p up to 6.