论文标题
戈尔迪戒指的LD稳定性
LD-stability for Goldie rings
论文作者
论文摘要
J. J Zhang引入的较低的超越程度是环理论和非交通性几何形状的重要非交换性，与经典的Gelfand-Kirillov超越程度密切相关。对于LD稳定代数，较低的超越程度与Gelfand-Kirillov维度一致。我们表明，以下代数是LD稳定的，并计算出较低的超越程度：仿生域的差异操作员的环，普遍包裹有限尺寸的代数超级词，符号反射代数，代数代数及其球形的subgebras及其较小的$ W $ w $ w $ w $ noterian noterand $ notery $ ainterian $ ainteriand $ ainter nyyy nyled nyled nyy nyle nyy nyy nyy nyy nyy nyy nyy nyled nyyl andery（条件），一些量子组。我们表明，较低的超越程度在有限群体和莫里塔对等方面相对于不变性的行为很好。给出了这些结果的应用。
The lower transcendence degree, introduced by J. J Zhang, is an important non-commutative invariant in ring theory and non-commutative geometry strongly connected to the classical Gelfand-Kirillov transcendence degree. For LD-stable algebras, the lower transcendence degree coincides with the Gelfand-Kirillov dimension. We show that the following algebras are LD-stable and compute their lower transcendence degrees: rings of differential operators of affine domains, universal enveloping algebras of finite dimensional Lie superalgebras, symplectic reflection algebras and their spherical subalgebras, finite $W$-algebras of type $A$, generalized Weyl algebras over Noetherian domain (under a mild condition), some quantum groups. We show that the lower transcendence degree behaves well with respect to the invariants by finite groups, and with respect to the Morita equivalence. Applications of these results are given.
