A -representation with no quantum symmetric algebra
- Volume: 10, Issue: 1, page 5-9
- ISSN: 1120-6330
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topRossi-Doria, Olivia. "A \( \mathcal{U}_{q} (\mathfrak{sl} (2)) \)-representation with no quantum symmetric algebra." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 10.1 (1999): 5-9. <http://eudml.org/doc/252276>.
@article{Rossi1999,
abstract = {We show by explicit calculations in the particular case of the 4-dimensional irreducible representation of \( \mathcal\{U\}\_\{q\} (\mathfrak\{sl\} (2)) \) that it is not always possible to generalize to the quantum case the notion of symmetric algebra of a Lie algebra representation.},
author = {Rossi-Doria, Olivia},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Quantized enveloping algebra; Representation; Symmetric algebra},
language = {eng},
month = {3},
number = {1},
pages = {5-9},
publisher = {Accademia Nazionale dei Lincei},
title = {A \( \mathcal\{U\}\_\{q\} (\mathfrak\{sl\} (2)) \)-representation with no quantum symmetric algebra},
url = {http://eudml.org/doc/252276},
volume = {10},
year = {1999},
}
TY - JOUR
AU - Rossi-Doria, Olivia
TI - A \( \mathcal{U}_{q} (\mathfrak{sl} (2)) \)-representation with no quantum symmetric algebra
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1999/3//
PB - Accademia Nazionale dei Lincei
VL - 10
IS - 1
SP - 5
EP - 9
AB - We show by explicit calculations in the particular case of the 4-dimensional irreducible representation of \( \mathcal{U}_{q} (\mathfrak{sl} (2)) \) that it is not always possible to generalize to the quantum case the notion of symmetric algebra of a Lie algebra representation.
LA - eng
KW - Quantized enveloping algebra; Representation; Symmetric algebra
UR - http://eudml.org/doc/252276
ER -
References
top- Drinfeld, V. G., Hopf algebras and quantum Yang-Baxter equation. Soviet. Math. Dokl., 32, 1985, 254-258. Zbl0588.17015MR802128
- Drinfeld, V. G., Quantum groups. Proc. ICM, Berkeley1986, 1, 798-820. MR934283
- Jimbo, M., A q-difference analogue of and the Yang-Baxter equation. Lett. Math. Phys., 10, 1985, 63-69. Zbl0587.17004MR797001DOI10.1007/BF00704588
- Kassel, C., Quantum groups. Graduate Texts in Math., vol. 155, Springer-Verlag, New York1995. Zbl0808.17003MR1321145DOI10.1007/978-1-4612-0783-2
- Yu, N., Quantized universal enveloping algebra, the Yang-Baxter equation and invariants of links I. LOMI, preprint 1987, no. E-4-87.
- Rosso, M., Finite-dimensional representations of the quantum analogue of the enveloping algebra of a complex simple Lie algebra. Comm. Math. Phys., 117, 1988, 581-593. Zbl0651.17008MR953821
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