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Representations of the q-deformed algebra U'_q(so_4)
We study the nonstandard -deformation of the universal
enveloping algebra obtained by deforming the defining relations
for skew-symmetric generators of . This algebra is used in
quantum gravity and algebraic topology. We construct a homomorphism of
to the certain nontrivial extension of the Drinfeld--Jimbo
quantum algebra 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 . It is proved that for not a root of
unity each irreducible finite dimensional representation of
is equivalent to one of these representations. We prove that every finite
dimensional representation of for not a root of unity is
completely reducible. It is shown how to construct (by using the homomorphism
) tensor products of irreducible representations of .
(Note that no Hopf algebra structure is known for .) These
tensor products are decomposed into irreducible constituents.Comment: 28 pages, LaTe
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