论文标题
融合产品的Gröbner基础
Gröbner bases for fusion products
论文作者
论文摘要
我们为B.〜feigin和S.〜loktev定义的融合产物的分析提供了一种新的方法，该方法在（截断的）当前谎言代数的表示理论中。我们将融合产物理解为使用格布纳（Gröbner）的非共同代数理论的变性，并概述了如何证明有关两个评估模块融合产物的定义关系的策略。我们以$ \ mathfrak {sl} _2（\ mathbb {c} [t]）$遵循此策略的结论，因此在这种情况下为猜想提供了另一个证据。
We provide a new approach towards the analysis of the fusion products defined by B.~Feigin and S.~Loktev in the representation theory of (truncated) current Lie algebras. We understand the fusion product as a degeneration using Gröbner theory of non-commutative algebras and outline a strategy on how to prove a conjecture about the defining relations for the fusion product of two evaluation modules. We conclude with following this strategy for $\mathfrak{sl}_2(\mathbb{C}[t]) $ and hence provide yet another proof for the conjecture in this case.
