论文标题
量子表示理论和Manin矩阵II：超级案例
Quantum Representation Theory and Manin matrices II: super case
论文作者
论文摘要
我们构建了量子表示理论的超级反应。描述了二次超级代数及其对它们的操作。我们还描述了一些重要的单体函子。我们证明，与有限生成的二次超级代数的子类别相对于有限生成的亚类别，分级超级代数的单体类别是共锁定的。引入了$（a，b）$ - manin矩阵的超级version，并与二次超级代数相关。我们定义了量子表示和量子线性作用的超级反复，将它们相互关联，并通过超曼宁矩阵描述它们。描述了一些对量子表示/量子线性作用的操作。我们展示了经典表示如何提高量子水平。
We construct super-version of Quantum Representation Theory. The quadratic super-algebras and operations on them are described. We also describe some important monoidal functors. We proved that the monoidal category of graded super-algebras with Manin product is coclosed relative to the subcategory of finitely generated quadratic super-algebras. The super-version of the $(A,B)$-Manin matrices is introduced and related with the quadratic super-algebras. We define a super-version of quantum representations and of quantum linear actions, relate them to each other and describe them by the super-Manin matrices. Some operations on quantum representations/quantum linear actions are described. We show how the classical representations lift to the quantum level.
