An Infinite-Dimensional □q-Module Obtained from the q-Shuffle Algebra for Affine sl₂

• Опубліковано в: : Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2020
• Автори: Post, Sarah, Terwilliger, Paul
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут математики НАН України 2020
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/210713
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: An Infinite-Dimensional □q-Module Obtained from the q-Shuffle Algebra for Affine sl₂. Sarah Post and Paul Terwilliger. SIGMA 16 (2020), 037, 35 pages

Let 𝔽 denote a field, and pick a nonzero q ∈ 𝔽 that is not a root of unity. Let ℤ₄ = ℤ/4ℤ denote the cyclic group of order 4. Define a unital associative 𝔽-algebra □q by generators {xᵢ}ᵢ∈ℤ4 and relations (qxᵢxᵢ₊₁ − q⁻¹xᵢ₊₁xᵢ)/(q−q⁻¹) = 1, x³ᵢxᵢ₊₂ − [3]qx²ᵢxᵢ + ₂xᵢ + [3]qxᵢxᵢ₊₂x²ᵢ − xᵢ₊₂x³ᵢ=0, where...