Contents

• Contents
• Introduction
  • Ring theory basics
  • Filtered & graded rings
  • Weyl, tensor & symmetric algebras
• Lie Algebras
  • Basic definitions
  • Nilpotent & solvable Lie algebras
• Universal Enveloping Algebras
  • Definition of $\mathcal{U}(\EuFrak{g})$
  • Poincare-Birkhoff-Witt Theorem
  • Properties of $\mathcal{U}(\EuFrak{g})$
• Prime Ideals
  • Primitive ideals
  • Ideal structure of $\mathcal{U}(\EuFrak{g})$
  • Characterization of primitive ideals
  • Prime and simple factors of $\mathcal{U}(\EuFrak{g})$
• Conclusion
• Bibliography
• References