Who was a Hungarian-American mathematician, physicist, and computer scientist that helped introduce a technique for using unbounded operators to study modules generated by a single vector?
Affiliated operator In mathematics, affiliated operators were introduced by Murray and von Neumann in the theory of von Neumann algebras as a technique for using unbounded operators to study modules generated by a single vector. Later Atiyah and Singer showed that index theorems for elliptic operators on closed manifolds with infinite fundamental group could naturally be phrased in terms of unbounded operators affiliated with the von Neumann algebra of the group. Algebraic properties of affiliated operators have proved important in L cohomology, an area between analysis and geometry that evolved from the study of such index theorems.
Monster vertex algebra The monster vertex algebra (or moonshine module) is a vertex algebra acted on by the monster group that was constructed by Igor Frenkel, James Lepowsky, and Arne Meurman. R. Borcherds used it to prove the monstrous moonshine conjectures, by applying the Goddard–Thorn theorem of string theory to construct the monster Lie algebra, an infinite-dimensional generalized Kac–Moody algebra acted on by the monster.