Wronskians as n-Lie multiplications

TL;DR

This paper investigates whether certain algebraic structures derived from associative commutative algebras with derivations, specifically Wronskian-based (k+1)-multiplications, possess (k+1)-Lie, k-left commutative, and homotopical (k+1)-Lie properties.

Contribution

It introduces a new class of algebras based on Wronskians and explores their potential (k+1)-Lie and related structures, extending previous results on Jacobian algebras.

Findings

Identification of conditions for (k+1)-Lie structures

Analysis of k-left commutativity in Wronskian algebras

Assessment of homotopical (k+1)-Lie properties

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.