Weak Faddeev–Takhtajan–Volkov algebras. Lattice 𝑊𝑛 algebras
https://doi.org/10.22405/2226-8383-2021-22-1-273-291
Abstract
In this paper, we will start by deliberating at our project’s historical general view and then we will try to construct a new Poisson bracket on our simplest example 𝑠𝑙2 and then we will try
to give a universal construction based on our universal variables and then will try to construct lattice 𝑊2 algebras which will play a key role in our other constructions on lattice 𝑊3 algebras
and finally we will try to find the only nontrivial dependent generator of our lattice 𝑊4 algebras and so on for lattice 𝑊𝑛 algebras
References
1. Antonov, A., Belov, A.A. and Chaltikian, K., 1997. ”Lattice conformal theories and their integrable perturbations.” Journal of Geometry and Physics, 22(4), pp.298-318.
2. Belov, A.A. and Chaltikian, K.D., 1993. ”Lattice analogues of W-algebras and classical integrable equations.” Physics Letters B, 309(3-4), pp.268-274.
3. Berenstein, A., 1996. ”Group-like elements in quantum groups, and Feigin’s conjecture.” arXiv preprint q-alg/9605016.
4. Caressa, P., 2000. ”The algebra of Poisson brackets.” In Young Algebra Seminar, Roma Tor Vergata.
5. Feigin, B.L. talk at RIMS 1992.
6. Faddeev, L. and Volkov, A.Y., 1993. ”Abelian current algebra and the Virasoro algebra on the lattice”. Physics Letters B, 315(3-4), pp.311-318.
7. Gainutdinov, A.M., Saleur, H. and Tipunin, I.Y., 2014. ”Lattice W-algebras and logarithmic CFTs”. Journal of Physics A: Mathematical and Theoretical, 47(49), p.495401.
8. Goursat, E., 1916. ”A Course in Mathematical Analysis: pt. 2. Differential equations.” [c1917 (Vol. 2). Dover Publications.
9. Hikami, K., 1997. ”Lattice WN algebra and its quantization.” Nuclear Physics B, 505(3), pp.749- 770.
10. Hikami, K. and Inoue, R., 1997. ”Classical lattice W algebras and integrable systems.” Journal of Physics A: Mathematical and General, 30(19), p.6911.
11. Hong, J. and Kang, S.J., 2002. ”Introduction to quantum groups and crystal bases” (Vol. 42).
12. American Mathematical Soc.. 12. Kassel, C., 2012. ”Quantum groups” (Vol. 155). Springer Science & Business Media.
13. Majid, S., 2002. ”A quantum groups primer” (Vol. 292). Cambridge University Press. 14. Pugay, Y.P., 1994. ”LatticeW algebras and quantum groups.” Theoretical and Mathematical
14. Physics, 100(1), pp.900-911.
15. Razavinia, F., 2016. ”Local coordinate systems on quantum flag manifolds.” arXiv preprint arXiv:1610.09443.
Review
For citations:
Razavinia F. Weak Faddeev–Takhtajan–Volkov algebras. Lattice 𝑊𝑛 algebras. Chebyshevskii Sbornik. 2021;22(1):273-291. (In Russ.) https://doi.org/10.22405/2226-8383-2021-22-1-273-291
Views:
347
Email this article 