Werner Heisenberg the lattice theory of crystals in 1921. While matrices were used in these cases, the algebra of matrices with their multiplication did not enter the picture as they did in the matrix formulation of quantum mechanics. In 1928, Albert Einstein nominated Heisenberg, Born, and Jordan for the Nobel Prize in Physics, The announcement of the Nobel Prize in Physics for 1932 was delayed until November 1933. It was at that time that it was announced Heisenberg had won the Prize for 1932 "for the creation of quantum mechanics, the application of which has, , led to the discovery of the
Heisenberg group group of a locally compact abelian group "K", equipped with a Haar measure. Such a group has a Pontrjagin dual formula_101, consisting of all continuous formula_102-valued characters on "K", which is also a locally compact abelian group if endowed with the compact-open topology. The Heisenberg group associated with the locally compact abelian group "K" is the subgroup of the unitary group of formula_103 generated by translations from "K" and multiplications by elements of formula_101. In more detail, the Hilbert space formula_103 consists of square-integrable complex-valued functions formula_106 on "K". The translations in "K" form a unitary representation of "K" as