Centers of universal enveloping algebras of Lie superalgebras in prime characteristic

Let $⋙={⋙}_{\text{bz}}+{⋙}_{\text{bo}}$ be a basic classical Lie superalgebra over an algebraically closed field $k$ of characteristic $p>2$, and $G$ be an algebraic supergroup satisfying $\text{Lie}(G)=⋙$, with the purely even subgroup $G_{\text{ev}}$ which is a reductive group. The center $\text{cz}:=\text{cz}(⋙)$ of the universal enveloping algebra of $⋙$ easily turns out to be a domain. In this paper, we prove that the quotient field of $\text{cz}$ coincides with that of the subalgebra generated by the $G_{\text{ev}}$-invariant ring ${\text{cz}}^{G_{\text{ev}}}$ of $\text{cz}$ and the $p$-center ${\text{cz}}_0$ of $U({⋙}_{\text{bz}})$.