Semilinear relations and *-representations of deformations of so(3)

Samoĭlenko, Yuriĭ ; Turowska, Lyudmila

Banach Center Publications, Tome 38 (1997), p. 21-40 / Harvested from The Polish Digital Mathematics Library

Résumé

We study a family of commuting selfadjoint operators $=(A_k)_{k=1}^n$, which satisfy, together with the operators of the family $=(B_j)_{j=1}^{n}$, semilinear relations $⅀ _{i} f_{ij}() B_j g_{ij}() = h()$, ($f_{ij}$, $g_{ij}$, $h_j: ℝ^n → ℂ$ are fixed Borel functions). The developed technique is used to investigate representations of deformations of the universal enveloping algebra U(so(3)), in particular, of some real forms of the Fairlie algebra $U_q^{\prime }(so(3))$.

Détail

Publié le : 1997-01-01

Zbl 1013.17504

EUDML-ID : urn:eudml:doc:252181

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