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

Janusz 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 -