Bell, Jason, Launois, Stephane, Nolan, Brendan (2017) A strong DixmierMoeglin equivalence for quantum Schubert cells. Journal of Algebra, 487 (1). pp. 269293. ISSN 00218693. (doi:10.1016/j.jalgebra.2017.06.005) (KAR id:62050)
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Official URL: http://dx.doi.org/10.1016/j.jalgebra.2017.06.005 
Abstract
Dixmier and Moeglin gave an algebraic condition and a topological condition for recognising the primitive ideals among the prime ideals of the universal enveloping algebra of a finitedimensional complex Lie algebra; they showed that the primitive, rational, and locally closed ideals coincide. In modern terminology, they showed that the universal enveloping algebra of a finitedimensional complex Lie algebra satisfies the Dixmier–Moeglin equivalence.
We define quantities which measure how “close” an arbitrary prime ideal of a noetherian algebra is to being primitive, rational, and locally closed; if every prime ideal is equally “close” to satisfying each of these three properties, then we say that the algebra satisfies the strong Dixmier–Moeglin equivalence . Using the example of the universal enveloping algebra of sl2(C), we show that the strong Dixmier–Moeglin equivalence is strictly stronger than the Dixmier–Moeglin equivalence.
For a simple complex Lie algebra g, a nonroot of unity q?0 in an infinite field K, and an element w of the Weyl group of g, De Concini, Kac, and Procesi have constructed a subalgebra Uq[w] of the quantised enveloping Kalgebra Uq(g). These quantum Schubert cells are known to satisfy the Dixmier–Moeglin equivalence and we show that they in fact satisfy the strong Dixmier–Moeglin equivalence. Along the way, we show that commutative affine domains, uniparameter quantum tori, and uniparameter quantum affine spaces satisfy the strong Dixmier–Moeglin equivalence.
Item Type:  Article 

DOI/Identification number:  10.1016/j.jalgebra.2017.06.005 
Uncontrolled keywords:  Prime ideals; primitive ideals; DixmierMoeglin equivalence; quantum Schubert cells 
Divisions:  Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science 
Depositing User:  Stephane Launois 
Date Deposited:  13 Jun 2017 08:29 UTC 
Last Modified:  04 Mar 2024 15:37 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/62050 (The current URI for this page, for reference purposes) 
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