Theoretical Perspectives on Representations of Plesken Lie Algebras
Keywords:
An prominent field of study related to Lie theory, representations of Lie groups and Lie algebras, has its origins in the work of Sophus Lie, who examined certain transformation groups that are now known as Lie groups.Abstract
An prominent field of study related to Lie theory, representations of Lie groups and Lie algebras, has its origins in the work of Sophus Lie, who examined certain transformation groups that are now known as Lie groups. Both Lie groups and Lie algebras are now fundamental to many areas of theoretical physics and mathematics. Compared to the Liegroup, the Lie algebra is more readily available since it is a linear entity. Wilhelm Killing (1847–1923) argued that categorising all (finite dimensional real) Lie algebras should come before classifying all group actions. It became evident from the slow development of Lie, Friedrich Engel (1861–1941), and Killing's theories that figuring out all basic Lie algebras was essential. Unless otherwise indicated, a Lie algebra is a finite dimensions over a field with characteristic zero in this article.
