Non-computability of K -theory for computably presented C * -algebras

Key Points

• The aim is to show the existence of a unital C*-algebra with a computable presentation that cannot be computably presented in its K-theory.
• Introduced an example of a unital C*-algebra A with a computable presentation.
• Analyzed the presentations of 0(A) and 1(A) to demonstrate their non-computability.
• Identified a specific unital C*-algebra A where neither 0(A) nor 1(A) has a computable presentation.
• Established the non-computability of K-theory in the context of the given C*-algebra.