Noncommutative Semialgebraic Sets in Nilpotent Variables

Details Noncommutative Semialgebraic Sets in Nilpotent Variables Noncommutative Semialgebraic Sets in Nilpotent Variables

2011-01-12

arxiv.org/abs/1101.2269v1

Mathematics

Operator Algebras

10 pages

Scientific paper

We solve the lifting problem in C^*-algebras for many sets of relations that include the relations x_j^{N_j} = 0 on each variable. The remaining relations must be of the form \| p(x_1,...,x_n) \| \leq 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 x^3=0, y^4=0, z^5=0, xx^*+yy^*+zz^* \leq 1. Thus we find more noncommutative semialgebraic sets that have the topology of noncommutative absolute retracts.

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