实超群的图解法
Diagrammatics for real supergroups
AI总结：
该研究引入两类分别推广有向、无向Brauer范畴的图解幺半超范畴，证明其对应超函子在中心实可除超代数下为满，得到多类实超群不变量理论第一基本定理及相关超范畴等价关系。
摘要：
我们引入两类图解幺半超范畴。第一类依赖于一个结合超代数，推广了有向Brauer范畴；第二类依赖于一个对合超代数，推广了无向Brauer范畴。这两类超范畴分别存在到一般线性超群、保持超埃尔米特形式的超群的超模超范畴的自然超函子。我们证明，当超代数是中心实可除超代数时，这些超函子是满的。由此，我们得到了一般线性、正交辛、奇辛、同分异构超群的所有实形式的不变量理论第一基本定理，还推导出复超群实形式上张量超模的幺半超范畴之间的等价关系。
英文摘要：
We introduce two families of diagrammatic monoidal supercategories. The first family, depending on an associative superalgebra, generalizes the oriented Brauer category. The second, depending on an involutive superalgebra, generalizes the unoriented Brauer category. These two families of supercategories admit natural superfunctors to supercategories of supermodules over general linear supergroups and supergroups preserving superhermitian forms, respectively. We show that these superfunctors are full when the superalgebra is a central real division superalgebra. As a consequence, we obtain first fundamental theorems of invariant theory for all real forms of the general linear, orthosymplectic, periplectic, and isomeric supergroups. We also deduce equivalences between monoidal supercategories of tensor supermodules over the real forms of a complex supergroup.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
