论文标题
不可约合的整合模块，用于由理性量子圆环协调的完整圆环谎言代数
Irreducible Integrable Modules for the full Toroidal Lie Algebras co-ordinated by Rational Quantum Torus
论文作者
论文摘要
令$ \ mathbb {c} _q $为与$（n+1）\ times（n+1）$合理量子矩阵$ q $相关的非交换laurent laurent多项式环。令$ \ mathfrak {sl} _d（\ mathbb {c} _q）\ oplus hc_1（\ mathbb {c} _q）$是lie subalgebra $ \ mathfrak {sl} {sl} _d} _d _d（\ mathbb {\ mathbb {\ mathbb {c} c} _q} _q} q} _q} q} $ $ \ mathfrak {gl} _d（\ mathbb {c} _q）$。现在，让我们采取Lie代数$τ= \ Mathfrak {gl} _d（\ Mathbb {c} _Q）\ oplus hc_1（\ Mathbb {c} _Q）$。令$ der（\ mathbb {c} _q）$为$ \ mathbb {c} _q $的所有派生的lie代数。现在，我们考虑Lie代数$ \tildeτ=τ\ rtimes der（\ mathbb {c} _q）$，称为由Ronical Quantum tori协调的完整的toroidal lie代数。在本文中，我们获得了不可约合的集成模块的分类，该模块具有有限的尺寸重量空间，用于$ \tildeτ$，在模块上具有非零中央动作。
Let $\mathbb{C}_q$ be a non-commutative Laurent polynomial ring associated with a $(n+1)\times (n+1)$ rational quantum matrix $q$. Let $\mathfrak{sl}_d(\mathbb{C}_q)\oplus HC_1(\mathbb{C}_q)$ be the universal central extension of Lie subalgebra $\mathfrak{sl}_d(\mathbb{C}_q)$ of $\mathfrak{gl}_d(\mathbb{C}_q)$. Now let us take the Lie algebra $τ=\mathfrak{gl}_d(\mathbb{C}_q)\oplus HC_1(\mathbb{C}_q)$. Let $Der(\mathbb{C}_q)$ be the Lie algebra of all derivations of $\mathbb{C}_q$. Now we consider the Lie algebra $\tildeτ=τ\rtimes Der(\mathbb{C}_q)$, called as full toroidal Lie algebra co-ordinated by rational quantum tori. In this paper we get a classification of irreducible integrable modules with finite dimensional weight spaces for $\tildeτ$ with nonzero central action on the modules.
