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

• Autorzy: Janusz Wysoczański
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 20C08: Hecke algebras and their representations
• 16T25: Yang-Baxter equations
• 17B37: Quantum groups (quantized enveloping algebras) and related deformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 89
• Numer: 1
• Strony: 323-327

Daty

wydano

2010

Twórcy

autor

Janusz Wysoczański

• Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Identyfikatory

DOI

10.4064/bc89-0-22