# On a cubic Hecke algebra associated with the quantum group ${U}_{q}\left(2\right)$

Banach Center Publications (2010)

- Volume: 89, Issue: 1, page 323-327
- ISSN: 0137-6934

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topJanusz Wysoczański. "On a cubic Hecke algebra associated with the quantum group $U_q(2)$." Banach Center Publications 89.1 (2010): 323-327. <http://eudml.org/doc/282373>.

@article{JanuszWysoczański2010,

abstract = {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 $h_j: = I_j ⊗ α ⊗ I_\{n-2-j\}$ on $(ℂ³)^\{⊗n\}$ 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.},

author = {Janusz Wysoczański},

journal = {Banach Center Publications},

keywords = {quantum groups; cubic Hecke algebras; Yang-Baxter equation},

language = {eng},

number = {1},

pages = {323-327},

title = {On a cubic Hecke algebra associated with the quantum group $U_q(2)$},

url = {http://eudml.org/doc/282373},

volume = {89},

year = {2010},

}

TY - JOUR

AU - Janusz Wysoczański

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

JO - Banach Center Publications

PY - 2010

VL - 89

IS - 1

SP - 323

EP - 327

AB - 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 $h_j: = I_j ⊗ α ⊗ I_{n-2-j}$ on $(ℂ³)^{⊗n}$ 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.

LA - eng

KW - quantum groups; cubic Hecke algebras; Yang-Baxter equation

UR - http://eudml.org/doc/282373

ER -

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