本项目将借鉴Brauer代数，特别是参数为零的Brauer代数，的理论、方法与技巧研究periplectic Brauer代数的结构、表示及其应用。具体言之，本项目将建立periplectic Brauer代数的fusion过程，由此确定（中心）本原幂等元和Morita等价分类，证明存在fussion过程的periplectic Brauer代数是胞腔代数；证明periplectic Brauer代数的中心是平凡的；证明periplectic版本的Gavarini猜想，研究periplectic Brauer代数的单模维数、构造及标准模同态；研究periplectic Brauer代数的分次结构与表示理论；构建periplectic版本的Schur-Weyl对偶理论，由此用periplectic Brauer代数理解periplectic李超代数的最高权表示和有限维可积表示范畴等。

In 2003, Moon introduced an algebra bearing resemblance to those of the Brauer algebra with parameter 0, which is called the periplectic Brauer algebra, as a tool to understand the mysterious representation theory of the periplectic Lie superalgebras. It has become apparent in recent years that many properties of the the Brauer algebras with parameter 0 have counterparts in the seting of periplectic Brauer algebras. A point that should be noted is that we don't know whether the periplectic Brauer algebra is a cellular algebra in the sense of Graham-Lehrer due to the missing of anti-involution, which is a standardly basis algebra in the sense of Du-Rui. On basis of the theory of the Brauer algebras with parameter 0, the project aims at investigating the structure, representations of periplectic Brauer algebras and its applications thoroughly. We will set up the fussion preocedure of the periplectic Brauer algebras, dertermine its (central) primitive idempotents, classification up to Morita equivalence, and its celluar structure. We will prove that the center of periplectic Brauers is trivial and the periplectic version of the Gavarini conjecture, which enalbes us to explore the structure and dimensions of simple modules of periplectic Brauer algebras. We will initate the study of the graded representation theory of periplectic Brauer algebras, i.e., we will provide the criterions of Koszul grading, graded hereditary, and graded cellularity of periplectic Brauer algebras. We will introduce the Schur algebra of periplectic Brauer algebra and establish the periplectic version of the Weyl-Schur duality. We expect that the project should lead to a better understanding of the structure, representations of peripletic Brauer algebra, and the representations of the periplectic Lie superalgebras.