English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We show that the complicated *-structure characterizing for positive q theU_qso(N)-covariant differential calculus on the non-commutative manifold R_q^Nboils down to similarity transformations involving the ribbon element of acentral extension of U_qso(N) and its formal square root v. Subspaces of thespaces of functions and of p-forms on R_q^N are made into Hilbert spaces byintroducing non-conventional ``weights'' in the integrals defining thecorresponding scalar products, namely suitable positive-definiteq-pseudodifferential operators realizing the action of v^{\pm 1}; this servesto make the partial q-derivatives antihermitean and the exterior coderivativeequal to the hermitean conjugate of the exterior derivative, as usual. There isa residual freedom in the choice of the weight m(r) along the `radialcoordinate' r. Unless we choose a constant m, then the square-integrablesfunctions/forms must fulfill an additional condition, namely their analyticcontinuations to the complex r plane can have poles only on the sites of somespecial lattice. Among the functions naturally selected by this condition thereare q-special functions with `quantized' free parameters.Comment: Latex file, 40 pages, 1 built in figure. Added references. Final  version to appear in Rev. Math. Phy

ON THE HERMITICITY OF q-DIFFERENTIAL OPERATORS AND FORMS ON THE QUANTUM EUCLIDEAN SPACES $\mathbb{R}_q^N$