TL;DR
This paper proves that nilpotent contractions in quotient C*-algebras can be lifted to nilpotent contractions in the original algebra, establishing projectivity of the universal C*-algebra generated by such contractions.
Contribution
It demonstrates that every nilpotent contraction in a quotient C*-algebra can be lifted, and shows the universal C*-algebra generated by a nilpotent contraction is projective.
Findings
Nilpotent contractions can be lifted in quotient C*-algebras.
Universal C*-algebra generated by a nilpotent contraction is projective.
Answers a question posed by T. Loring.
Abstract
It is proved that that every nilpotent contraction in a quotient C*-algebra can be lifted to a nilpotent contraction. As a consequence we get that the universal C*-algebra generated by a nilpotent contraction is projective. This answers the question posed by T. Loring.
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