论文标题
二次代数的manin矩阵
Manin Matrices for Quadratic Algebras
论文作者
论文摘要
我们对MANIN矩阵的一般定义就任意二次代数的定义。我们建立了他们的主要特性，并根据类别理论给出了解释。对于一般的Manin矩阵，未成年人的概念被推广。我们举例说明了Manin矩阵，与LAX运营商的关系，并为一些未成年人获得公式。特别是，我们考虑了A. Molev引入的类型$ B $，$ C $和$ D $的Manin矩阵及其与Brauer代数的关系。还考虑了无限维MANIN矩阵及其与LAX操作员的联系。
We give a general definition of Manin matrices for arbitrary quadratic algebras in terms of idempotents. We establish their main properties and give their interpretation in terms of the category theory. The notion of minors is generalised for a general Manin matrix. We give some examples of Manin matrices, their relations with Lax operators and obtain the formulae for some minors. In particular, we consider Manin matrices of the types $B$, $C$ and $D$ introduced by A. Molev and their relation with Brauer algebras. Infinite-dimensional Manin matrices and their connection with Lax operators are also considered.
