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

Yuriĭ Samoĭlenko; Lyudmila Turowska

ArticleOriginal scientific text

Title

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

Authors ¹, ¹

Affiliations

Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivska Str., Kiev, 252601 Ukraine

Abstract

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_{i j} () B_{j} g_{i j} () = h ()

, (

f_{i j}

,

g_{i j}

,

h_{j} : ℝ^{n} \to 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}' (s o (3))

.

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Title

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

Affiliations

Abstract

Bibliography