The Prime ideal Stratification and The Automorphism Group of U⁺_r,s(B₂)

2011/09/12 by Xin Tang, Tang, Xin · 1 citation
Mathematics · #Advanced Topics in Algebra #Commutative Algebra and Its Applications #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.QA #math.RA #math.RT

paper · pdf · doi:10.48550/arxiv.1109.2640

arxiv created 2011/09/12 · openalex publication_date 2011/09/12 · arxiv updated 2011/09/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let \mathfrak g be a finite dimensional complex simple Lie algebra, and let r,s∈ ℂ^∗ be transcendental over ℚ such that r^msⁿ=1 implies m=n=0. We will obtain some basic properties of the two-parameter quantized enveloping algebra U_r,s⁺(\mathfrak g). In particular, we will verify that the algebra U_r,s⁺(\mathfrak g) satisfies many nice properties such as having normal separation, catenarity and Dixmier-Moeglin equivalence. We shall study a concrete example, the algebra U_r,s⁺(B₂) in detail. We will first determine the normal elements, prime ideals and primitive ideals for the algebra U_r,s⁺(B₂), and study their stratifications. Then we will prove that the algebra automorphism group of the algebra U_r,s⁺(B₂) is isomorphic to (ℂ^∗)².

Cited by

• Simple Modules and PI Structure of the Two-Parameter Quantized Algebra U⁺_r,s(B₂)

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