 

Terry A. Loring and Tatiana Shulman
Noncommutative semialgebraic sets in nilpotent variables view print


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


Abstract
We solve the lifting problem in C*algebras for many sets of
relations that include the relations x_{j}^{Nj}=0 for all variables.
The remaining relations must be of the form
∥p(x_{1},...,x_{n})∥ ≦ 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*≦1.
Thus we find more noncommutative semialgebraic sets that have the
topology of noncommutative absolute retracts.


Acknowledgements
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.
loring@math.unm.edu
Tatiana Shulman:
Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK2100 Copenhagen O, Denmark
shulman@math.ku.dk

