java class object and Types

Given a class

public class A {
  public static int classVal;
}

During run-time, does the type A become a reference to a class Object?

public static void main(String[] args) {
  A a = new A(); 
  A.classVal = 100;
  A.classVal = 200;
}

if A.classVal is a reference to static Class variable, then is A a reference to an Object that represents the class?

does a.getClass() refer to the same object as A?

To clarify

if A.classVal is a reference, and A is nothing more than a name, does a class just become part of a lookup table that uses the class name as a key? I am trying to understand what happens to a class at run-time.