Representations of the q-deformed algebra U'_q(so_4)

Details Representations of the q-deformed algebra U'_q(so_4) Representations of the q-deformed algebra U'_q(so_4)

2001-02-05

arxiv.org/abs/math/0102036v1

Mathematics

Quantum Algebra

28 pages, LaTeX

Scientific paper

We study the nonstandard $q$-deformation $U'_q({\rm so}_4)$ of the universal enveloping algebra $U({\rm so}_4)$ obtained by deforming the defining relations for skew-symmetric generators of $U({\rm so}_4)$. This algebra is used in quantum gravity and algebraic topology. We construct a homomorphism $\phi$ of $U'_q({\rm so}_4)$ to the certain nontrivial extension of the Drinfeld--Jimbo quantum algebra $U_q({\rm sl}_2)^{\otimes 2}$ 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 $U'_q({\rm so}_4)$. It is proved that for $q$ not a root of unity each irreducible finite dimensional representation of $U'_q({\rm so}_4)$ is equivalent to one of these representations. We prove that every finite dimensional representation of $U'_q({\rm so}_4)$ for $q$ not a root of unity is completely reducible. It is shown how to construct (by using the homomorphism $\phi$) tensor products of irreducible representations of $U'_q({\rm so}_4)$. (Note that no Hopf algebra structure is known for $U'_q({\rm so}_4)$.) These tensor products are decomposed into irreducible constituents.

Affiliated with

Also associated with

No associations

Rating

Representations of the q-deformed algebra U'_q(so_4) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Representations of the q-deformed algebra U'_q(so_4), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Representations of the q-deformed algebra U'_q(so_4) will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-104840