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Quotient Gradings and the Intrinsic Fundamental Group by Ginosar, Yuval; Schnabel, Ofir is a scholarly article available to read on EtoBox.

What is Quotient Gradings and the Intrinsic Fundamental Group about?

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 $A=\mathbb{C} ^5$.

Author

Ginosar, Yuval; Schnabel, Ofir

Published

2022

Language

EN