We introduce a new quantized enveloping superalgebra \({\mathfrak {U}}_q{\mathfrak {p}}_n\) attached to the Lie superalgebra \({\mathfrak {p}}_n\) of type P. The superalgebra \({\mathfrak {U}}_q{\mathfrak {p}}_n\) is a quantization of a Lie bisuperalgebra structure on \({\mathfrak {p}}_n\), and we study some of its basic properties. We also introduce the periplectic q-Brauer algebra and prove that it is the centralizer of the \({\mathfrak {U}}_q{\mathfrak {p}}_n\)-module structure on \({\mathbb {C}}(n|n)^{\otimes l}\). We end by proposing a definition for a new periplectic q-Schur superalgebra.

我们引入了一个新的量化包络超代数\({\mathfrak {U}}_q{\mathfrak {p}}_n\)附加到类型P的李超代数\({\mathfrak {p}}_n\)。超代数\({\mathfrak {U}}_q{\mathfrak {p}}_n\)是李双超代数结构在\({\mathfrak {p}}_n\)上的量化，我们研究了它的一些基本属性。我们还引入了绕折q -Brauer 代数并证明它是\({\mathfrak {U}}_q{\mathfrak {p}}_n\) -模块结构在\({\mathbb {C} }(n|n)^{\otimes l}\)。最后，我们提出了一个新的绕折q -Schur 超代数的定义。