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.

J. J Zhang提出的较低超越度是环理论中的重要非交换不变性，并且与经典Gelfand-Kirillov超越度有很强的联系。对于LD稳定的代数，较低的超越度与Gelfand-Kirillov维度重合。我们证明以下代数是LD稳定的，并计算出它们的较低超越度：仿射域的微分算子环，有限维Lie超级代数的通用包络代数，辛反射代数及其球面子代数，A型有限W代数，在Noether域上（在温和条件下）的广义Weyl代数，一些量子基团。我们表明，较低的超越度对于有限组的不变量以及森田等价而言表现良好。给出了这些结果的应用。