On a cubic Hecke algebra associated with the quantum group $U_q(2)$

Janusz Wysoczański

On a cubic Hecke algebra associated with the quantum group

U_{q} (2)

Janusz Wysoczański

Banach Center Publications, Tome 89 (2010), p. 323-327 / Harvested from The Polish Digital Mathematics Library

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Résumé

We define an operator α on ℂ³ ⊗ ℂ³ associated with the quantum group $U_{q} (2)$ , which satisfies the Yang-Baxter equation and a cubic equation (α² - 1)(α + q²) = 0. This operator can be extended to a family of operators $h_{j} : = I_{j} \otimes α \otimes I_{n - 2 - j}$ on ${(ℂ ³)}^{\otimes n}$ with 0 ≤ j ≤ n - 2. These operators generate the cubic Hecke algebra $ℋ_{q, n} (2)$ associated with the quantum group $U_{q} (2)$ . The purpose of this note is to present the construction.

Publié le : 2010-01-01

Zbl 1261.17016

EUDML-ID : urn:eudml:doc:282373

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     author = {Janusz Wysocza\'nski},
     title = {On a cubic Hecke algebra associated with the quantum group $U\_q(2)$
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     journal = {Banach Center Publications},
     volume = {89},
     year = {2010},
     pages = {323-327},
     zbl = {1261.17016},
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Janusz Wysoczański. On a cubic Hecke algebra associated with the quantum group $U_q(2)$
            . Banach Center Publications, Tome 89 (2010) pp. 323-327. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc89-0-22/