We study the symmetric powers of four algebras: -oscillator algebra, -Weyl algebra, -Weyl algebra and . We provide explicit formulae as well as combinatorial interpretation for the normal coordinates of products of arbitrary elements in the above algebras.
@article{AMBP_2004__11_2_187_0, author = {Rafael D{\'\i}az and Eddy Pariguan}, title = {Symmetric quantum {Weyl} algebras}, journal = {Annales Math\'ematiques Blaise Pascal}, pages = {187--203}, publisher = {Annales math\'ematiques Blaise Pascal}, volume = {11}, number = {2}, year = {2004}, doi = {10.5802/ambp.192}, mrnumber = {2109607}, zbl = {02205936}, language = {en}, url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.192/} }
TY - JOUR TI - Symmetric quantum Weyl algebras JO - Annales Mathématiques Blaise Pascal PY - 2004 DA - 2004/// SP - 187 EP - 203 VL - 11 IS - 2 PB - Annales mathématiques Blaise Pascal UR - https://ambp.centre-mersenne.org/articles/10.5802/ambp.192/ UR - https://www.ams.org/mathscinet-getitem?mr=2109607 UR - https://zbmath.org/?q=an%3A02205936 UR - https://doi.org/10.5802/ambp.192 DO - 10.5802/ambp.192 LA - en ID - AMBP_2004__11_2_187_0 ER -
Rafael Díaz; Eddy Pariguan. Symmetric quantum Weyl algebras. Annales Mathématiques Blaise Pascal, Volume 11 (2004) no. 2, pp. 187-203. doi : 10.5802/ambp.192. https://ambp.centre-mersenne.org/articles/10.5802/ambp.192/
[1] Fixed rings of the Weyl algebra , Journal of algebra, Volume 130 (1990), pp. 83-96 | Article | MR: 1045737 | Zbl: 0695.16022
[2] Quantum groups, Springer-Velarg, New York, 1995 | MR: 1321145 | Zbl: 0808.17003
[3] Noncommutative Solitons on Orbifolds (2001) (hep-th/0101199)
[4] Deformation Quantization of Poisson Manifolds I (1997) (math. q-alg/97090401)
[5] Algebras of functions on Quantum groups. Part I, Mathematical surveys and monographs, Volume 56 (1996) | Zbl: 0923.17017
[6] Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism, Invent. Math, Volume 147 (2002) no. 2, pp. 243-348 | Article | MR: 1881922 | Zbl: 1061.16032
[7] On the foundations of combinatorial theory. VII: Symmetric functions through the theory of distribution and occupancy, Gian-Carlo Rota on Combinatorics. Introductory papers and commentaries (1995), pp. 402-422
[8] Quantum symmetric functions (2003) (math.QA/0312494)
[9] Super, quantum and non-commutative species (2004) (Work in progress)
[10] Noncommutative Solitons, J. High Energy Phys. JHEP, Volume 05-020 (2000) | MR: 1768736 | Zbl: 0989.81612
[11] Phys.Lett. A 196, 1994 (Number 29, Volume 126)
[12] Infinite dimensional Lie algebras., Cambridge University Press, New York, 1990 | MR: 1104219 | Zbl: 0716.17022
[13] Quantum Calculus, Springer-Velarg, New York, 2002 | MR: 1865777 | Zbl: 0986.05001
Cited by Sources: