The Euclidean Hopf Algebra U q ( e N ) and its fundamental Hilbert space representations

Abstract

We construct the Euclidean Hopf algebra Uq(e ) dual of Fun(Rq >⊳SOq−1(N)) by realizing it as a subalgebra of the differential algebra Diff(Rq ) on the quantum Euclidean space Rq ; in fact, we extend our previous realization [1] of Uq−1(so(N)) within Diff(R N q ) through the introduction of q-derivatives as generators of q-translations. The fundamental… (More)

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