Drinfel'd Twist and q-Deforming Maps for Lie Group Covariant Heisenberg Algebras

Details Drinfel'd Twist and q-Deforming Maps for Lie Group Covariant Heisenberg Algebras Drinfel'd Twist and q-Deforming Maps for Lie Group Covariant Heisenberg Algebras

1997-08-18

arxiv.org/abs/q-alg/9708017v3

Rev.Math.Phys. 12 (2000) 327-359

Mathematics

Quantum Algebra

latex file, 35 pages, no figures. Final version to appear in Rev. Math. Phys

Scientific paper

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.

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