Noncommutative Semialgebraic Sets in Nilpotent Variables
Abstract
We solve the lifting problem in C*-algebras for many sets of relations that include the relations xjNj = 0 on each variable. The remaining relations must be of the form \| p(x1,...,xn) \| ≤ C for C a positive constant and p a noncommutative *-polynomial that is in some sense homogeneous. For example, we prove liftability for the set of relations x3=0, y4=0, z5=0, xx*+yy*+zz* ≤ 1. Thus we find more noncommutative semialgebraic sets that have the topology of noncommutative absolute retracts.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.