The centre of the modular super Yangian Ym|n$Y_{m|n}$

摘要

The present paper is devoted to studying the super Yangian Ym|n$Y_{m|n}$ associated to the general linear Lie superalgebra glm|n$\mathfrak {gl}_{m|n}$ over a field of positive characteristic. We extend Drinfeld-type presentations of Ym|n$Y_{m|n}$ and the special super Yangian SYm|n$SY_{m|n}$ to positive characteristic. Moreover, the centre Z(Ym|n)$Z(Y_{m|n})$ of Ym|n$Y_{m|n}$ is described: it is generated by its Harish-Chandra centre together with a large p$p$-centre. We also study the p$p$-centre of SYm|n$SY_{m|n}$ and provide another description of the p$p$-centre of Ym|n$Y_{m|n}$ in terms of the RTT generators.

关键词