LD-stability for Goldie rings

Author(s)

Futorny, Vyacheslav ^{[1, 2]} ; Schwarz, Joao ^[1] ; Shestakov, Ivan ^[1]

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, Caixa Postal 66281, BR-05315970 Sao Paulo - Brazil

^[2] SUSTech, Int Ctr Math, Shenzhen - Peoples R China

• Document type: Journal article
• Source: Journal of Pure and Applied Algebra; v. 225, n. 11 NOV 2021.
• Web of Science Citations: 0

Abstract

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. (C) 2021 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 18/23690-6 - Structures, representations, and applications of algebraic systems
• Grantee: Ivan Chestakov
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 18/18146-5 - Ore Domainas: localizations, invariants and representations.
• Grantee: João Fernando Schwarz
• Support Opportunities: Scholarships in Brazil - Post-Doctoral