Most books at this level rely on deep ideas from outside Lie Theory, such as the inverse function theorem. However, this book actually proves simplicity ofthe classical Lie algebras can be done by basic matrix arithmetic, and there is an amazing elementary proof of Campbell-Baker-Hausdorff due to Eichler in 1968. The naive approach to Lie theory is due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics,particularly the results of linear algebra. To compensate for the lack of technical power which is inherent to the naïve approach, the end-of-chapter discussions introduce important results beyond those proved in the book, as part ofan informal sketch of Lie theory and its history. While naive methods might not afford the same insights as more sophisticated methods, they do offer another insight that is often undervalued—some important theorems are not as difficult as they look! Makes some basic Lie theory accessible Unique choice of approach and topics Introduces an advanced topic to undergraduates, at just the right pace Authors includes exercises and examples INDICE: Preface.- Geometry of complex numbers and quaternions.- Groups.- Generalized rotation groups.- The exponential map.- The tangent space.- Structure of lie algebras.- The matrix logarithm.- Topology.- Simply-connected lie groups.- Bibliography.- Index.
- ISBN: 978-0-387-78214-0
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 200
- Fecha Publicación: 01/07/2008
- Nº Volúmenes: 1
- Idioma: Inglés
- Inicio /
- MATEMÁTICAS /
- ÁLGEBRA