The Razak-Jacelon algebra 
is the simple separable nuclear stably projectionless 
-algebra with trivial 
-theory obtained as an inductive limit of Razak building blocks,
with a unique tracial state and no unbounded densely
defined traces. Stably projectionless means that 
has no nonzero projection, where 
is the compact operators on a separable infinite-dimensional
Hilbert space. The algebra is nonunital. Simple
inductive limits of Razak building blocks are classified by their extended
trace cone together with the subset of bounded traces of norm at most 1 (Jacelon
2013, Theorem 1.1).
Razak-Jacelon Algebra
See also
Extended Trace Cone, Jiang-Su Stability, Nuclear C-Star-AlgebraExplore with Wolfram|Alpha
References
Jacelon, B. "A Simple, Monotracial, Stably Projectionless
-Algebra."
J. London Math. Soc. 87, 365-383, 2013. https://doi.org/10.1112/jlms/jds049.
Cite this as:
Weisstein, Eric W. "Razak-Jacelon Algebra." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Razak-JacelonAlgebra.html