The projection form of the Kadison-Kaplansky conjecture asserts that the reduced group C*-algebra
of a torsion-free discrete group has no projections
except 0 and 1. A projection here is
an element 
of the algebra satisfying 
. This is a scalar-algebra
assertion, rather than absence of nontrivial projections
in all matrix algebras over it.
Kadison-Kaplansky Conjecture
See also
Baum-Connes Conjecture, Group Algebra, Group C*-Algebra, Idempotent, Torsion-Free GroupExplore with Wolfram|Alpha
References
Lück, W. and Reich, H. "The Baum-Connes and the Farrell-Jones Conjectures in
- and 
-Theory." In Handbook of K-Theory, Vol. 2
(Ed. E. M. Friedlander and D. R. Grayson). Berlin, Germany: Springer,
pp. 703-842, 2005. https://doi.org/10.1007/978-3-540-27855-9_15.
Cite this as:
Weisstein, Eric W. "Kadison-Kaplansky Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Kadison-KaplanskyConjecture.html