Quantum Heisenberg groups and Sklyanin algebras
arXiv:hep-th/9305036 · doi:10.1007/BF00761709
Abstract
We define new quantizations of the Heisenberg group by introducing new quantizations in the universal enveloping algebra of its Lie algebra. Matrix coefficients of the Stone--von Neumann representation are preserved by these new multiplications on the algebra of functions on the Heisenberg group. Some of the new quantizations provide also a new multiplication in the algebra of theta functions; we obtain in this way Sklyanin algebras.
13 pages