6 problems

For an associative algebra $\mathcal{A}$, let $\mathrm{Prim}^{\mathrm{fin}}(\mathcal{A})$ denote the set of primitive ideals of finite codimension. Let $\mathcal{U}_{0}$ and…

Let $\mathfrak{g}$ be the Lie superalgebra and $e$ the nilpotent element defining the finite $W$-superalgebra $U(\mathfrak{g},e)$. Let $Z(U(\mathfrak{g}))$ and…

Let $\mathfrak{g}$ be a basic Lie superalgebra over $\mathbb{C}$, let $e\in\mathfrak{g}_{\bar 0}$ be nilpotent, and let $\chi$ be the corresponding linear function on…

Let $\mathfrak{g}=\mathfrak{g}_{\bar 0}+\mathfrak{g}_{\bar 1}$ be a basic Lie superalgebra over $\mathbb{C}$, let $e\in\mathfrak{g}_{\bar 0}$ be nilpotent, and let $\mathsf{r}$ be…

Let $\mathfrak{g}$ be a basic Lie superalgebra over $\mathbb{C}$, let $e\in\mathfrak{g}_{\bar 0}$ be nilpotent, and set $d_1=\dim\mathfrak{g}_{\bar 1}-\dim\mathfrak{g}^e_{\bar 1}$.…

A finite $W$-superalgebra is an associative superalgebra whose finite-dimensional representations are considered over the field of complex numbers. Its detecting parity determines…