8 problems

Let $F$ be a field of zero characteristic, and let $J$ be a simple Jordan superalgebra over $F$ with nonzero odd part. The possible superalgebras include $H(A,*)$, where $(A,*)$ is…

Let $F$ be a field of zero characteristic, and let $J$ be a simple Jordan superalgebra over $F$ with nonzero odd part. A Jordan superalgebra is $i$-special if it is a homomorphic i…

The $\mathfrak{f}(4)$ dynamical supersymmetry conjecture. There exists a superized Landau problem whose dynamical supersymmetry, meaning its superconformal Lie algebra, is…

Let $P=P_0\oplus P_1$ be a Poisson superalgebra, and let $\mathrm{Kan}(P)=P\oplus\bar P$ be its Kantor double, a Jordan superalgebra. The functor $\mathrm{Kan}$ sends Poisson $P$-s…

Let $R={\mathbb Z}[x]/(x^2-1)$, let $a_n^s=\overline{\dim}J_n(D_1|D_2)$, and write … Define … and … The generating-function conjecture. The sequence $a_n^s$ is the unique solution…

Let $R={\mathbb Z}[x]/(x^2-1)$, and let $a_n^s=\overline{\dim}J_n(D_1|D_2)$ and $b_n^s=\overline{\dim}{\mathcal B}^s_n(J(D_1|D_2))$ be sequences in $R$. Write … Define…

Let $J(D_1|D_2)$ be the free Jordan superalgebra with $D_1+D_2\geq 1$. Let $G$ be the acting algebraic group, let ${\mathcal R}^s(G)$ be the relevant super representation ring, let…

Let $J(D_1|D_2)$ be the free Jordan superalgebra and let $\mathfrak{sl}_2J(D_1|D_2)$ denote its associated Tits–Kantor–Koecher Lie superalgebra. For $r\geq 2$, write…