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JOURNALS // Funktsional'nyi Analiz i ego Prilozheniya

Funktsional. Anal. i Prilozhen., 1993, Volume 27, Issue 1, Pages 12–24 (Mi faa678)

$\mathbb{Z}$-Graded Trigonometric Lie Subalgebras in $\widehat{A}_\infty$, $\widehat{B}_\infty$, $\widehat{C}_\infty$, and $\widehat{D}_\infty$ and Their Vertex Operator Representations
M. I. Golenishcheva-Kutuzova, D. R. Lebedev

References

1. Fairlie D., Fletcher P., Zachos C., “Trigonometric structure constants for new infinite-dimensional algebras”, Phys. Lett. B, 218:2 (1989), 203–206  crossref  mathscinet  zmath  adsnasa  scopus
2. Saveliev M. V., Vershik A. M., “Continual analogs of contragredient Lie algebras”, Comm. Math. Phys., 126:2, 367–378  crossref  mathscinet  zmath  scopus
3. Saveliev M. V., Vershik A. M., “New examples of continuum graded Lie algebras”, Phys. Lett. A, 143 (1990), 121–128  crossref  mathscinet  adsnasa  scopus
4. Lebedev D., Orlov A., Pakuliak S., Zabrodin A., “Nonlocal integrable equations of the Toda hierarchy”, Phys. Lett. A, 160 (1991), 166–172  crossref  mathscinet  adsnasa  scopus
5. Lebedev D., Pakuliak S., “Zakharov–Shabat technique with quantized spectral parameter in the theory of integrable models”, Phys. Lett. A, 160 (1991), 173–178  crossref  mathscinet  adsnasa  scopus
6. Hoppe J., Olshanetsky M., Theisen S., Dynamical system on trigonometrical algebras, Preprint KA–THEP–10/91
7. Floratos E. G., “Spin wedge and vertex operators representations of trigonometric algebras and their central extensions”, Phys. Lett. B, 232 (1989), 467–474  crossref  mathscinet  adsnasa  scopus
8. Golenischeva-Kutuzova M., Lebedev D., “Predstavlenie vershinnymi operatorami sinus-algebry Veilya–Moiala–Ferli”, Pisma v ZhETF, 52:10 (1990), 1164–1167
9. Kac V., Infinite-dimensional Lie algebras, Cambrige Univ. Press, 1991  mathscinet
10. Kac V., Kazhdan D., Lepowsky J., Wilson R., “Realization of the basic representation of the Euclidean Lie algebras”, Adv. in Math., 42 (1981), 83–112  crossref  mathscinet  zmath  scopus
11. Connes A., Rieffel M., “Yang–Mills for non-commutative two tori”, Contemp. Math., 62, 1978, 237–266  crossref  mathscinet
12. Connes A., “Non-commutative differential geometry”, Publ. Math., 1985, no. 62, 41–144  crossref  mathscinet  zmath
13. Frenkel I. V., Jing N., “Vertex representations of quantum affine algebras”, Proc. Natl. Acad. Sci. USA, 85 (1988), 9373–9377  crossref  mathscinet  zmath  adsnasa
14. Golenischeva-Kutuzova M., Lebedev D., “Trigonometricheskie podalgebry Li v $X_\infty=A_\infty$ (sootv. $B_\infty$, $C_\infty$, $D_\infty$) i ikh predstavleniya vershinnymi operatorami”, Pisma v ZhETF, 52:8 (1991), 473–476
15. Hoppe J., “$\operatorname{Diff}_AT^2$ and the curvature of some infinite dimensional manifolds”, Phys. Lett. B, 215 (1988), 706–710  crossref  mathscinet  adsnasa  scopus
16. Vershik A. M., “Continuum roots system Lie algebras” (to appear)


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