Spectra and catenarity of multiparameter quantum Schubert cells

TL;DR

This paper investigates the structure of multiparameter quantum Schubert cell algebras, classifying their spectra, prime ideals, and proving properties like normal separation and catenarity across various parameters and characteristics.

Contribution

It provides a comprehensive classification of spectra, prime ideals, and proves catenarity for a broad family of multiparameter quantum Schubert cell algebras, extending known algebraic frameworks.

Findings

Classified spectra of all such algebras.

Constructed prime ideals via explicit localizations.

Proved spectra are normally separated and algebras are catenary.

Abstract

We study the ring theory of the multiparameter deformations of the quantum Schubert cell algebras obtained from 2-cocycle twists. This is a large family, which extends the Artin-Schelter-Tate algebras of twisted quantum matrices. We classify set theoretically the spectra of all such multiparameter quantum Schubert cell algebras, construct each of their prime ideals by contracting from explicit normal localizations, and prove formulas for the dimensions of their Goodearl-Letzter strata for base fields of arbitrary characteristic and all deformation parameters that are not roots of unity. Furthermore, we prove that the spectra of these algebras are normally separated and that all such algebras are catenary.