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The periplectic Brauer algebra

We study the periplectic Brauer algebra introduced by Moon in the study of invariant theory for periplectic Lie superalgebras. We determine when the algebra is quasi‐hereditary, when it admits a quasi‐hereditary 1‐cover and, for fields of characteristic zero, describes the block decomposition. To achieve this, we also develop theories of Jucys–Murphy elements, Bratteli diagrams, Murphy bases, obtain a Humphreys‐BGG reciprocity relation and determine some decomposition multiplicities of cell modules. As an application, we determine the blocks in the category of finite dimensional integrable modules of the periplectic Lie superalgebra.