dorsal/arxiv
View SchemaDrinfel'd Twist and q-Deforming Maps for Lie Group Covariant Heisenberg Algebras
| Authors | Gaetano Fiore |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9708017 |
| URL | https://arxiv.org/abs/q-alg/9708017 |
| DOI | 10.1142/S0129055X00000125 |
| Journal | Rev.Math.Phys.12:327-359,2000 |
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.
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"abstract": "Any deformation of a Weyl or Clifford algebra can be realized through a\nchange of generators in the undeformed algebra. q-Deformations of Weyl or\nClifford algebrae that were covariant under the action of a simple Lie algebra\ng are characterized by their being covariant under the action of the quantum\ngroup $U_q g$. We present a systematic procedure for determining all possible\ncorresponding changes of generators, together with the corresponding\nrealizations of the $U_q g$-action. The intriguing relation between\ng-invariants and $U_q g$-invariants suggests that these changes of generators\nmight be employed to simplify the dynamics of some g-covariant quantum physical\nsystems.",
"arxiv_id": "q-alg/9708017",
"authors": [
"Gaetano Fiore"
],
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"q-alg",
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"doi": "10.1142/S0129055X00000125",
"journal_ref": "Rev.Math.Phys.12:327-359,2000",
"title": "Drinfel\u0027d Twist and q-Deforming Maps for Lie Group Covariant Heisenberg Algebras",
"url": "https://arxiv.org/abs/q-alg/9708017"
},
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