Wronskians as n-Lie multiplications

A.S. Dzhumadil'daev

Wronskians as n-Lie multiplications

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arxiv math/0202043 v1 pith:2XI64E3U submitted 2002-02-05 math.RA math-phmath.MP

A.S. Dzhumadil'daev This is my paper · ORCID

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keywords wedgealgebracommutativen-liealgebrasassociativeconsiderdefined

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abstract

Filipov proved that Jacobian algebra is n-Lie. In our paper we consider algebras defined on associative commutative algebra U with derivation $\der$ by (k+1)-multiplication $V^{0,1,...,k}=\der^0\wedge\der^1\wedge...\wedge \der^k$ (Wronskian). We study whether they have (k+1)-Lie, k-left commutative and homotopical (k+1)-Lie structures.

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Explicit class of finite-dimensional polynomial algebras with Wronskians over $\mathbb{R}^d$ as $N$-ary Lie brackets: beyond $\mathfrak{sl}(2)$
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Explicit classification of all finite-dimensional polynomial SH-Lie algebras over R^d or C^d using complete generalized Wronskians of order k as N-ary brackets, together with a factorization formula for the associated...

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