Simple classical groups of Lie type are determined by their character degrees

TL;DR

This paper proves that nonabelian simple classical groups of Lie type can be uniquely identified by examining the structure of their complex group algebras, providing a new way to distinguish these groups.

Contribution

It establishes that the structure of complex group algebras uniquely determines nonabelian simple classical groups of Lie type, a novel identification method.

Findings

Nonabelian simple classical groups are uniquely determined by their complex group algebras.

The structure of the complex group algebra encodes enough information to distinguish these groups.

This result advances understanding of the relationship between group structure and algebraic representations.

Abstract

In this paper, we will show that nonabelian simple classical groups of Lie type are uniquely determined by the structure of their complex group algebras.