论文标题
商等级和内在基本小组
Quotient gradings and the intrinsic fundamental group
论文作者
论文摘要
商的分级课程是计算代数$ a $的内在基本组$π_1（a）$的重要参与者。为了研究有限维半神经复合体代数的商等级，足以了解扭曲等级的商等级。我们使用Mackey的阻塞类建立此类商的分级结构。然后，对于矩阵代数$ a = m_n（\ mathbb {c}）$，我们将牙套，群体理论的拉格朗日和基本交叉产品的概念联系起来。我们还设法计算对角线代数的固有基本组$ a = \ mathbb {c} ^4 $和$ a = \ mathbb {c} ^5 $。
Quotient grading classes are essential participants in the computation of the intrinsic fundamental group $π_1(A)$ of an algebra $A$. In order to study quotient gradings of a finite-dimensional semisimple complex algebra $A$ it is sufficient to understand the quotient gradings of twisted gradings. We establish the graded structure of such quotients using Mackey's obstruction class. Then, for matrix algebras $A=M_n(\mathbb{C})$ we tie up the concepts of braces, group-theoretic Lagrangians and elementary crossed products. We also manage to compute the intrinsic fundamental group of the diagonal algebras $A=\mathbb{C} ^4$ and $A=\mathbb{C} ^5$.
