Representations, Classification and Contractions of 3-Dimensional Lie Algebras

Introduction This purpose of this paper is to summarize research done in the theory of Lie algebras, with attention directed towards contractions of Lie algebras. It is written in the style of an introduction to these topics for undergraduates familiar with (though not necessarily proficient in) linear and abstract algebra. It is separated into three sections: section (1) describes the basic definitions and properties of Lie algebras in an abstract setting; section (2) narrows the discussion to specific linear Lie algebras and their properties, which are the focus of the remaining section; section (3) defines and describes a particular type of a general process known as contractions between linear Lie algebras, focusing on those properties of Lie algebras that remain invariant under this process.