On the double of the (restricted) super Jordan plane in odd characteristic

Abstract

In this paper we consider the super Jordan plane, a braided Hopf algebra introduced--to the best of our knowledge--in [AAH1], and its restricted version in odd characteristic introduced in [AAH2]. We show that their Drinfeld doubles give rise naturally to Hopf superalgebras justifying a posteriori the adjective super given in loc. cit. These Hopf superalgebras are extensions of super commutative ones by the enveloping, respectively restricted enveloping, algebra of osp(1|2).