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

Yuriĭ Samoĭlenko; Lyudmila Turowska

Banach Center Publications (1997)

  • Volume: 40, Issue: 1, page 21-40
  • ISSN: 0137-6934

Abstract

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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 : n 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 ) ) .

How to cite

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Samoĭlenko, Yuriĭ, and Turowska, Lyudmila. "Semilinear relations and *-representations of deformations of so(3)." Banach Center Publications 40.1 (1997): 21-40. <http://eudml.org/doc/252181>.

@article{Samoĭlenko1997,
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 $⅀ _\{i\} f_\{ij\}() B_j g_\{ij\}() = h()$, ($f_\{ij\}$, $g_\{ij\}$, $h_j: ℝ^n → ℂ$ 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 $U_q^\{\prime \}(so(3))$.},
author = {Samoĭlenko, Yuriĭ, Turowska, Lyudmila},
journal = {Banach Center Publications},
language = {eng},
number = {1},
pages = {21-40},
title = {Semilinear relations and *-representations of deformations of so(3)},
url = {http://eudml.org/doc/252181},
volume = {40},
year = {1997},
}

TY - JOUR
AU - Samoĭlenko, Yuriĭ
AU - Turowska, Lyudmila
TI - Semilinear relations and *-representations of deformations of so(3)
JO - Banach Center Publications
PY - 1997
VL - 40
IS - 1
SP - 21
EP - 40
AB - 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 $U_q^{\prime }(so(3))$.
LA - eng
UR - http://eudml.org/doc/252181
ER -

References

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