New York Journal of Mathematics
Volume 18 (2012) 361-372


Terry A. Loring and Tatiana Shulman

Noncommutative semialgebraic sets in nilpotent variables

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Published: June 2, 2012
Keywords: C*-algebra, relation, projective, lifting.
Subject: 46L85, 47B99

We solve the lifting problem in C*-algebras for many sets of relations that include the relations xjNj=0 for all variables. 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.


This work was partially supported by a grant from the Simons Foundation (208723 to Loring), by the Efroymson fund at UNM, and by the NordForsk Research Network "Operator Algebras and Dynamics'' (grant 11580).

Author information

Terry A. Loring:
Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, USA.

Tatiana Shulman:
Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen O, Denmark