Polynomials a_{j N}[x], 1 <j<N, of degree deg a_j = N are shown to be closed w.r.t. action of the N-ary bracket [a₁, ..., a_N] = W(a₁,...,a_N ), where W denotes the Wronskian determinant. This bracket is proved to induce the homotopical N-Lie algebra structure on the polynomials _N[x] of degree N, so that an extended Jacobi identity (with 2^N-1 summands) holds; the case N = 2 is the Lie bracket in sl₂() satisfying the Jacobi identity.

The property of the Wronskian determinants to compose the homotopical N-Lie algebras is proved to hold for arbitrary analytic functions a_j [[x]], thus extending the former result. The identity [[^i₁ ...^i_k+1,^j₁ ...^j_l+1]]^RN = 0 is discussed, where is a derivation and [[^.,^.]]^RN is the Richardson-Nijenhuis bracket.

The notion of the Wronskian determinant is generalized to the case of n independent variables: (x¹,...,xⁿ) ⁿ, so that the resulting concept preserves the homotopical N-Lie Jacobi identity.

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