Symmetric quantum Weyl algebras
Annales mathématiques Blaise Pascal, Tome 11 (2004) no. 2, pp. 187-203.

We study the symmetric powers of four algebras: q-oscillator algebra, q-Weyl algebra, h-Weyl algebra and U(𝔰𝔩 2 ). We provide explicit formulae as well as combinatorial interpretation for the normal coordinates of products of arbitrary elements in the above algebras.

DOI : 10.5802/ambp.192
Díaz, Rafael 1 ; Pariguan, Eddy 2

1 Instituto Venezolano de Inves- tigaciones Científicas Departamento de Matemáticas Altos de Pipe. Caracas 21827 Venezuela
2 Universidad Central de Venezue- la Departamento de Matemáticas Los Chaguaramos Caracas 1020 Venezuela
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Díaz, Rafael; Pariguan, Eddy. Symmetric quantum Weyl algebras. Annales mathématiques Blaise Pascal, Tome 11 (2004) no. 2, pp. 187-203. doi : 10.5802/ambp.192. http://www.numdam.org/articles/10.5802/ambp.192/

[1] Alev, J.; Hodges, T.J.; Velez, J.D. Fixed rings of the Weyl algebra A 1 (), Journal of algebra, Volume 130 (1990), pp. 83-96 | DOI | MR | Zbl

[2] Kassel, Christian Quantum groups, Springer-Velarg, New York, 1995 | MR | Zbl

[3] Martinec, Emil; Moore, Gregory Noncommutative Solitons on Orbifolds (2001) (hep-th/0101199)

[4] Kontsevich, M. Deformation Quantization of Poisson Manifolds I (1997) (math. q-alg/97090401)

[5] Korogodski, Leonid; Soibelman., Yan Algebras of functions on Quantum groups. Part I, Mathematical surveys and monographs, Volume 56 (1996) | Zbl

[6] Etingof, Pavel; Ginzburg, Victor Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism, Invent. Math, Volume 147 (2002) no. 2, pp. 243-348 | DOI | MR | Zbl

[7] Doubilet, Peter 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] Díaz, Rafael; Pariguan, Eddy Quantum symmetric functions (2003) (math.QA/0312494)

[9] Díaz, Rafael; Pariguan, Eddy Super, quantum and non-commutative species (2004) (Work in progress)

[10] Gopakumar, Rajesh; Minwalla, Shiraz; Strominger, Andrew Noncommutative Solitons, J. High Energy Phys. JHEP, Volume 05-020 (2000) | MR | Zbl

[11] Solomon, A.I. Phys.Lett. A 196, 1994 (Number 29, Volume 126)

[12] Kac, Victor Infinite dimensional Lie algebras., Cambridge University Press, New York, 1990 | MR | Zbl

[13] Kac, Victor; Cheung, Pokman Quantum Calculus, Springer-Velarg, New York, 2002 | MR | Zbl

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