Representations of SO(5)q are constructed explicitly on the Chevalley basis. The classical representations, once obtained on this basis, are very simply deformed for arbitrary q, generic, and root of unity. This is in sharp contrast to the classical canonical Gelfand–Zetlin (GZ) representations which lead to problems, studied elsewhere, in q deformations for orthogonal (though not for unitary) algebras. Our results are limited to irreducible representations labeled by three variable parameters, the maximal number being four. Within this restriction it is shown how to construct all representations for all q’s. The contraction of the Chevalley generators (e2,f2) leads to an easily obtained complete Hopf algebra. The structure of the contracted algebra is quite different, even at the classical level, from the familiar E(4), the four‐dimensional Euclidean algebra, obtained on contracting the generator J45 in the GZ formalism. The contracted representations are given. The SO(5)q representations have their own interest. Moreover they lead to a consistent Hopf algebra and representations for the nonsemisimple contracted case, for all q.

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