Conformal field theory
The Hilbert space of physical states is a unitary module of the Virasoro algebra corresponding to a fixed value of "c". Stability requires that the energy spectrum of the Hamiltonian be nonnegative. The modules of interest are the highest weight modules of the Virasoro algebra.
Calkin algebra
In functional analysis, the Calkin algebra, named after John Wilson Calkin, is the quotient of "B"("H"), the ring of bounded linear operators on a separable infinite-dimensional Hilbert space "H", by the ideal "K"("H") of compact operators. Here the addition in "B"("H") is addition of operators and the multiplication in "B"("H") is composition of operators; it is easy to verify that these operations make "B"("H") into a ring. When scalar multiplication is also included, "B"("H") becomes in fact an algebra over the same field over which "H" is a Hilbert space.