The Automorphism Groups and Derivation Algebras of Two-Dimensional Algebras

Ahmed H,Rakhimov I,Bekbaev U

doi:10.4172/1736-4337.1000290

Abstract

The automorphism groups and derivation algebras of all two-dimensional algebras over algebraically closed fields are described.

Highlights

There is a long history and an extended study of the automorphism groups of algebras
The study of the automorphism groups and derivation algebras is of a big interest due to the importance of them in the study of structure of algebras
In the present paper we describe the groups of automorphisms and derivation algebras of all those listed algebras

Summary

Introduction

There is a long history and an extended study of the automorphism groups of algebras. Over an algebraically closed field (Char( )≠2 and 3), any nontrivial 2-dimensional algebra is isomorphic to only one of the following algebras listed by their matrices of structure constants: Over an algebraically closed field (Char( )=2), any non-trivial 2-dimensional algebra is isomorphic to only one of the following algebras listed by their matrices of structure constants:

Results

Conclusion