Vern
Paulsen,
Pure
Math
Department,
University
of
Waterloo
“Quotients
of
Operator
Systems,
Nuclearity,
and
Lifting
Problems”
We introduce the concept of quotients of operator systems. We then provide some key examples, including representations of the operator systems spanned by the generators of certain free groups and the generators of the Cuntz algebras as quotients of matrix subsystems. We then show how such a representation can be used to convert questions about equality of minimal and maximal tensor products into lifting problems. We apply these ideas to the given representation of the generators of the Cuntz algebra to prove that nuclearity of the Cuntz algebras is equivalent to a solutions existing for certain lifting problems. Finally, we give a new proof of the nuclearity of the Cuntz algebra by solving this lifting problem.
MC 5417