A Deleting Derivations Algorithm for Quantum Nilpotent Algebras at Roots of Unity
Year: 2024
Type: article
Abstract: This paper extends an algorithm and canonical embedding in [6] to a large class of quantum algebras. It applies to iterated Ore extensions over a field satisfying some suitable assumptions which cover those of Cauchon’s original setting but also allows for roots of unity. The extended algorithm constructs a quantum affine space A ′ from the original quantum algebra A via a series of change of variables within the division ring of fractions Frac ( A ) . The canonical embedding takes a completely prime ideal P ⊲ A to a completely prime ideal Q ⊲ A ′ such that when A is a PI algebra, PI - deg ( A / P ) = PI - deg ( A ′ / Q ) . When the quantum parameter is a root of unity, combining our construction with results from [2] allows us to state an explicit formula for the PI degree of completely prime quotient algebras. This paper ends with a method to construct a maximum dimensional irreducible representation of A / P given a suitable irreducible representation of A ′ / Q when A is PI.
Source: Annals of representation theory
DOI: 10.5802/art.19
Authors: Stéphane Launois, Samuel A. Lopes, Alexandra Rogers
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404106085