Quotient gradings and the intrinsic fundamental group
| Autor: | Ginosar, Yuval, Schnabel, Ofir |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Quotient grading classes are essential participants in the computation of the intrinsic fundamental group $\pi_1(A)$ 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 $A=\mathbb{C} ^5$. Comment: 33 pages |
| Databáze: | arXiv |
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