FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 1, PAGES 159-180

Associative homotopy Lie algebras and Wronskians

A. V. Kiselev

Abstract

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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 $n$³ 1 independent variables.

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Last modified: April 27, 2005