Lifting algebraic contractions in C*-algebras

TL;DR

This paper demonstrates that the universal C*-algebra associated with polynomial relations is semiprojective, residually finite-dimensional, and has trivial extension group, advancing understanding of algebraic structures in operator algebras.

Contribution

It establishes new properties of universal C*-algebras for polynomial relations, including semiprojectivity and residual finite-dimensionality.

Findings

Universal C*-algebras of polynomial relations are semiprojective.

These algebras are residually finite-dimensional.

They have trivial extension groups.

Abstract

Let p be a polynomial in one variable. It is shown that the universal C*-algebra of the relation p(x)=0, \|x\| \le C is semiprojective, residually finite-dimensional and has trivial extension group.