Is there a Relationship between Quantum Groups and Lie Groups?

Question

I know that the Lie Group is all about continuous transformation groups.
I know that the quantum group denotes various kinds of noncommutative algebra with additional structure.
Transformation group is commutative group or Abelian group right?
But I need to know what is a ralationship between a Quantum Groups and a Lie Groups.
Can be Quantum Group as a Lie Group?
Also I dont know is there any Quantum Groups which is Discrete Group?
Can you show me sample?

Answer 1

Quantum groups are not groups, nor are these Hopf algebras (which is what they are) directly associated to any groups (as it the case of Lie algebras).