Lie Algebras

Poisson geometry lies at the cusp of noncommutative algebra and differential geometry, with natural and important links to classical physics and quantum mechanics. This book presents an introduction to the subject from a small group of leading researchers, and the result is a volume accessible to graduate students or experts from other fields. The contributions are: Poisson Geometry and Morita Equivalence by Bursztyn and Weinstein; Formality and Star Products by Cattaneo; Lie Groupoids, Sheaves and Cohomology by Moerdijk and Mrcun; Geometric Methods in Representation Theory by Schmid; Deformation Theory: A Powerful Tool in Physics Modelling by Sternheimer ch. 1. Basic concepts -- ch. 2. Solvable and nilpotent lie algebras -- ch. 3. Cartan's criterion and its consequences -- ch. 4. Split semi-simple lie algebras -- ch. 5. Universal enveloping algebras -- ch. 6. The theorem of Ado-Iwasawa -- ch. 7. Classification of irreducible modules -- ch. 8. Characters of the irreducible modules -- ch. [...]9. Automorphisms -- ch. 10. simple lie algebras over an arbitrary field