Launois, Stephane, Lecoutre, Cesar (2016) Poisson Deleting Derivations Algorithm and Poisson Spectrum. Communications in Algebra, 45 (3). pp. 12941313. ISSN 00927872. (doi:10.1080/00927872.2016.1175619) (KAR id:44211)
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Official URL: http://dx.doi.org/10.1080/00927872.2016.1175619 
Abstract
Cauchon [5 Cauchon, G. (2003). Effacement des dérivations et spectres premiers des algèbres quantiques. J. Algebra 260(2):476–518.
[CrossRef], [Web of Science ®]
] introduced the socalled deleting derivations algorithm. This algorithm was first used in noncommutative algebra to prove catenarity in generic quantum matrices, and then to show that torusinvariant primes in these algebras are generated by quantum minors. Since then this algorithm has been used in various contexts. In particular, the matrix version makes a bridge between torusinvariant primes in generic quantum matrices, torus orbits of symplectic leaves in matrix Poisson varieties and totally nonnegative cells in totally nonnegative matrix varieties [12 Goodearl, K. R., Launois, S., Lenagan, T. (2011). Torus invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves. Math. Z. 269(1):29–45.
[CrossRef], [Web of Science ®]
]. This led to recent progress in the study of totally nonnegative matrices such as new recognition tests [18 Launois, S., Lenagan, T. (2014). E?cient recognition of totally nonnegative matrix cells. Found. Comput. Math. 14:371–387.
[CrossRef], [Web of Science ®]
]. The aim of this article is to develop a Poisson version of the deleting derivations algorithm to study the Poisson spectra of the members of a class
Item Type:  Article 

DOI/Identification number:  10.1080/00927872.2016.1175619 
Uncontrolled keywords:  Poisson Algebra, Poisson Dixmier–Moeglin equivalence, Poisson spectrum 
Subjects:  Q Science > QA Mathematics (inc Computing science) 
Divisions:  Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science 
Depositing User:  Stephane Launois 
Date Deposited:  10 Nov 2014 11:19 UTC 
Last Modified:  08 Dec 2022 21:37 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/44211 (The current URI for this page, for reference purposes) 
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