C*-algebra
Banach *-algebra such that |𝑥*𝑥|=|𝑥||𝑥*|=|𝑥|²
von Neumann algebra
unital *-algebra of bounded operators on a Hilbert space closed in the weak operator topology
fuzzy sphere
noncommutative space (C*-algebra) generated by hermitian su(2) representations on an N-dimensional Hilbert space; as N → ∞, this converges to the commutative sphere (the algebra of spherical harmonics)
noncommutative torus
free unital C*-algebra generated by two generators U and V with UV=exp(iθ)VU, with θ irrational
compact quantum group
unital separable C*-algebra 𝐶 equipped with a coassociatve homomorphism Δ satisfying certain conditions
locally compact quantum group
relatively new C*-algebraic approach toward quantum groups
multiplier algebra
largest unital C*-algebra that contains a given C*-algebra as an ideal in a nondegenerate way