The criteria for automorphisms on finite-dimensional algebras

Abstract

In this paper, we will establish a criterion for automorphisms of finite-dimensional algebras. As an application, we will describe all automorphisms of the single-parameter generalized quaternion algebra. Additionally, we will obtain all automorphisms of Sweedler's 4-dimensional Hopf algebra.

Keywords

• hopf algebra
• matrix
• automorphism
• quaternion