Geodesic
Covariant structure constants for a deformed oscillator algebra
Teoretičeskaâ i matematičeskaâ fizika, Tome 193 (2017) no. 1, pp. 3-14 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We obtain $sl_2$-covariant expressions for the structure constants of the deformed oscillator algebra $Aq(2,\nu)$.
Mots-clés : structure constant
Keywords: deformed oscillator, higher-spin algebra, hypergeometric function. 
@article{TMF_2017_193_1_a0,
     author = {A. V. Koribut},
     title = {Covariant structure constants for a~deformed oscillator algebra},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {3--14},
     year = {2017},
     volume = {193},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_193_1_a0/}
}
TY  - JOUR
AU  - A. V. Koribut
TI  - Covariant structure constants for a deformed oscillator algebra
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2017
SP  - 3
EP  - 14
VL  - 193
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2017_193_1_a0/
LA  - ru
ID  - TMF_2017_193_1_a0
ER  - 
%0 Journal Article
%A A. V. Koribut
%T Covariant structure constants for a deformed oscillator algebra
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2017
%P 3-14
%V 193
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2017_193_1_a0/
%G ru
%F TMF_2017_193_1_a0
A. V. Koribut. Covariant structure constants for a deformed oscillator algebra. Teoretičeskaâ i matematičeskaâ fizika, Tome 193 (2017) no. 1, pp. 3-14. http://geodesic.mathdoc.fr/item/TMF_2017_193_1_a0/

[1] E. P. Wigner, “Do the equations of motion determine the quantum mechanical commutation relations?”, Phys. Rev., 77:5 (1950), 711–712 | DOI | Zbl

[2] M. A. Vasiliev, “Higher spin algebras and quantization on the sphere and hyperboloid”, Internat. J. Modern Phys. A, 6:7 (1991), 1115–1135 | DOI | MR | Zbl

[3] M. A. Vasilev, “Kvantovanie na sfere i superalgebry vysshikh spinov”, Pisma v ZhETF, 50:8 (1989), 344–347 | MR

[4] E. Bergshoeff, M. P. Blencowe, K. S. Stelle, “Area-preserving diffeomorphisms and higher-spin algebras”, Commun. Math. Phys., 128:2 (1990), 213–230 | DOI | MR | Zbl

[5] M. A. Vasiliev, “Consistent equation for interacting gauge fields of all spins in ${(3+1)}$-dimensions”, Phys. Lett. B, 243:4 (1990), 378–382 | DOI | MR | Zbl

[6] M. A. Vasiliev, “Nonlinear equations for symmetric massless higher spin fields in $(A)dS_d$”, Phys. Lett. B, 567:1 (2003), 139–151, arXiv: hep-th/0304049 | DOI | MR | Zbl

[7] C. N. Pope, X. Shen, L. J. Romans, “$W_\infty$ and the Racah–Wigner algebra”, Nucl. Phys. B, 339:1 (1990), 191–221 | DOI | MR

[8] E. Bergshoeff, M. A. Vasiliev, B. de Wit, “The super-$W_\infty(\lambda)$ algebra”, Phys. Lett. B, 256:2 (1991), 199–205 | DOI | MR | Zbl

[9] E. Bergshoeff, B. de Wit, M. A. Vasiliev, “The structure of the super-$W_\infty(\lambda)$ algebra”, Nucl. Phys. B, 366:2 (1991), 315–346 | DOI | MR

[10] M. R. Gaberdiel, R. Gopakumar, “Minimal model holography”, J. Phys. A: Math. Theor., 46:21 (2013), 214002, 47 pp., arXiv: 1207.6697 | DOI | MR | Zbl

[11] E. S. Fradkin, V. Ya. Linetsky, “Supersymmetric Racah basis, family of infinite-dimensional superalgebras, $\mathrm{SU}(\infty+1|\infty)$ and related 2D models”, Modern Phys. Lett. A, 6:7 (1991), 617–633 | DOI | MR | Zbl

[12] ;po0 E. Joung, K. Mkrtchyan, “Notes on higher-spin algebras: minimal representations and structure constants”, JHEP, 05 (2014), 103, 34 pp., arXiv: 1401.7977 | DOI | MR

[13] L. J. Slater, Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge, 1966 | MR