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- W2263103162 abstract "An algebra homomorphism $psi$ from the q-deformed algebra $U_q({rm iso}_2)$ with generating elements $I$, $T_1$, $T_2$ and defining relations $[I,T_2]_q=T_1$, $[T_1,I]_q=T_2$, $[T_2,T_1]_q=0$ (where $[A,B]_q=q^{1/2}AB-q^{-1/2}BA$) to the extension ${hat U}_q({rm m}_2)$ of the Hopf algebra $U_q({rm m}_2)$ is constructed. The algebra $U_q({rm iso}_2)$ at $q=1$ leads to the Lie algebra ${rm iso}_2 sim {rm m}_2$ of the group ISO(2) of motions of the Euclidean plane. The Hopf algebra $U_q({rm m}_2)$ is treated as a Hopf $q$-deformation of the universal enveloping algebra of ${rm iso}_2$ and is well-known in the literature. Not all irreducible representations of $U_q({rm m}_2)$ can be extended to representations of the extension ${hat U}_q({rm m}_2)$. Composing the homomorphism $psi$ with irreducible representations of ${hat U}_q({rm m}_2)$ we obtain representations of $U_q({rm iso}_2)$. Not all of these representations of $U_q({rm iso}_2)$ are irreducible. The reducible representations of $U_q({rm iso}_2)$ are decomposed into irreducible components. In this way we obtain all irreducible representations of $U_q({rm iso}_2)$ when $q$ is not a root of unity. A part of these representations turns into irreducible representations of the Lie algebra iso$_2$ when $qto 1$. Representations of the other part have no classical analogue." @default.
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- W2263103162 date "1999-01-01" @default.
- W2263103162 modified "2023-09-26" @default.
- W2263103162 title "Representations of theq-deformed algebraUq(iso2)" @default.
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- W2263103162 doi "https://doi.org/10.1088/0305-4470/32/25/310" @default.
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