8 problems

Poisson $n$-Lie algebra construction conjecture. Then $(\mathcal A, \cdot, [-,\dots,-])$ forms a Poisson $n$-Lie algebra.

Let $p=0$ and $n>2$. Consider the polynomial algebra $K[x_1,\ldots,x_n]$ with the Jacobian $n$-ary operation $Jac_n^S$, and, in the Poisson case, with its commutative product…

Let $n\geq 2$ be an integer. Let $(L,\cdot,[\cdot,\ldots,\cdot])$ be a transposed Poisson $n$-Lie algebra, and let $D$ be a derivation of both $(L,\cdot)$ and…

Let $n\geq 2$ be an integer and let $(L,\cdot,\mu_n)$ be a transposed Poisson $n$-Lie algebra. Let $D$ be a derivation of both $(L,\cdot)$ and $(L,\mu_n)$. For…

Let $\mathfrak{g}$ be a Lie algebra and let $\mathfrak{g}_\tau$ denote the $(n+1)$-Lie algebra induced from $\mathfrak{g}$ by a trace $\tau$. Write $Z^1(\mathfrak{g},\mathfrak{g})$…

Pozhidaev's conjecture. For any reductive finite-dimensional $n$-Lie algebra $L$ over an algebraically closed field of characteristic $0$, there exists an associative algebra $A$ s…

Pozhidaev's conjecture. Such an associative enveloping algebra exists for the simple finite-dimensional $n$-Lie algebra for every $n$.

A 3-Lie algebra is an algebra with a skew-symmetric trilinear bracket satisfying the generalized Jacobi identity, and a metric is a positive-definite invariant symmetric bilinear f…