Twist deformations for generalized Heisenberg algebras
arXiv:math/0001136 · doi:10.1142/9789812793263_0007
Abstract
Multidimensional Heisenberg algebras, whose creation and annihilation operators are the N-dimensional vectors, can be injected into simple Lie algebras g. It is demonstrated that the spectrum of their deformations can be investigated using chains of extended Jordanian twists applied to U(g). In the case of U(sl(N)) (for N>5) the two-dimensional Heisenberg subalgebras have nine deformed costructures connected by four "internal" and "external" twists composing the commutative diagram.
12 pages, Latex, to be published in the Proceedings of the XIV-th Symposium, Karpacz, Sept. 99