Drinfel'd Twist and q-Deforming Maps for Lie Group Covariant Heisenberg Algebras
Abstract
Any deformation of a Weyl or Clifford algebra can be realized through a change of generators in the undeformed algebra. q-Deformations of Weyl or Clifford algebrae that were covariant under the action of a simple Lie algebra g are characterized by their being covariant under the action of the quantum group
U
q
g
. We present a systematic procedure for determining all possible corresponding changes of generators, together with the corresponding realizations of the
U
q
g
-action. The intriguing relation between g-invariants and
U
q
g
-invariants suggests that these changes of generators might be employed to simplify the dynamics of some g-covariant quantum physical systems.