Quantized enveloping superalgebra of type $P$

Abstract

We introduce a new quantized enveloping superalgebra Uqpn attached to the Lie superalgebra pn of type P . The superalgebra Uqpn is a quantization of a Lie bisuperalgebra structure on pn 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 Uqpn-module structure on C(n|n) ⊗l . We end by proposing a definition for a new periplectic q-Schur superalgebra.