论文标题
周期性$ Q $ -BRAUER类别
The periplectic $q$-Brauer category
论文作者
论文摘要
我们介绍了特征不可或缺的$ 2 $的整体域，介绍了PRICLECTIC $ Q $ -BRAUER类别。这是一个严格的单类超类，可以被视为PRICLECTIC BRAUER类别的$ Q $ analogue。我们证明，Perioldic $ Q $ -BRAUER类别在Brundan-Stroppel的意义上承认了分裂的三角分解。当接地环是一个代数封闭的字段时，对Brundan和Stroppel的意义上，周期性$ Q $ -BRAUER类别的本地有限维右右模块类别是一个完全有限分层的类别。我们证明，[1]中定义的PRICLICTIC $ Q $ -BRAUER代数是同构的同构代数代数。此外，在DU和RUI的意义上，PRICLICEC $ Q $ -BRAUER代数是一个基于标准的代数。我们就jucys-murphy构建了jucys-murphy的基础，以相对于一个称为jucys-murphy元素的通勤元素的亲本$ q $ -Brauer代数。通过他们，我们将块类别$ q $ brauer类别和周围$ q $ -brauer代数的块分类为一般情况。我们的结果表明，在任何代数封闭的字段上，同时$ q $ brauer类别和周围的$ q $ -Brauer代数始终始终都不是半imimple。
We introduce the periplectic $q$-Brauer category over an integral domain of characteristic not $2$. This is a strict monoidal supercategory and can be considered as a $q$-analogue of the periplectic Brauer category. We prove that the periplectic $q$-Brauer category admits a split triangular decomposition in the sense of Brundan-Stroppel. When the ground ring is an algebraically closed field, the category of locally finite dimensional right modules for the periplectic $q$-Brauer category is an upper finite fully stratified category in the sense of Brundan and Stroppel. We prove that periplectic $q$-Brauer algebras defined in [1] are isomorphic to endomorphism algebras in the periplectic $q$-Brauer category. Furthermore, a periplectic $q$-Brauer algebra is a standardly based algebra in the sense of Du and Rui. We construct Jucys-Murphy basis for any standard module of the periplectic $q$-Brauer algebra with respect to a family of commutative elements called Jucys-Murphy elements. Via them, we classify blocks for both periplectic $q$-Brauer category and periplectic $q$-Brauer algebras in generic case. Our result shows that both periplectic $q$-Brauer category and periplectic $q$-Brauer algebras are always not semisimple over any algebraically closed field.
