Degree of Parabolic Quantum Groups - Dipartimento di Matematica ...

Contents v
In the second and third chapter, we describe the slight knowledge of
algebra with trace and quasi polynomial algebra. These are the instruments
necessary in order to describe the theory of the representations of Uǫ and
Uǫ(p). Moreover we describe how to calculate the degree of quasi polynomial
algebra.
This concludes the first part of the thesis. In the second part, we will be
studying the theory of quantum groups.
In chapter 4 we recall the main definitions and the main properties of
quantum universal enveloping algebras associated to a semisimple complex
Lie algebra g, and we consider how to calculate the degree of Uǫ(g) and Uǫ(b).
The last chapter is dedicated to the definition of quantum enveloping
algebra associated to a parabolic subalgebra p of g and the proof of the
formula for the degree.