Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
42 (2001), S. 5389-5416
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
We study the nonstandard q-deformation Uq′(so4) of the universal enveloping algebra U(so4) obtained by deforming the defining relations for skew-symmetric generators of U(so4). This algebra is used in quantum gravity and algebraic topology. We construct a homomorphism φ of Uq′(so4) to the certain nontrivial extension of the Drinfeld–Jimbo quantum algebra Uq(sl2)⊗2 and show that this homomorphism is an isomorphism. By using this homomorphism we construct irreducible finite-dimensional representations of the classical type and of the nonclassical type for the algebra Uq′(so4). It is proved that for q not a root of unity each irreducible finite-dimensional representation of Uq′(so4) is equivalent to one of these representations. We prove that every finite-dimensional representation of Uq′(so4) for q not a root of unity is completely reducible. It is shown how to construct (by using the homomorphism φ) tensor products of irreducible representations of Uq′(so4). [Note that no Hopf algebra structure is known for Uq′(so4).] These tensor products are decomposed into irreducible constituents. © 2001 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.1402631
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