# Poisson Deleting Derivations Algorithm and Poisson Spectrum

Launois, Stephane, Lecoutre, Cesar (2016) Poisson Deleting Derivations Algorithm and Poisson Spectrum. Communications in Algebra, 45 (3). pp. 1294-1313. ISSN 0092-7872. (doi:10.1080/00927872.2016.1175619)

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## 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 so-called deleting derivations algorithm. This algorithm was first used in noncommutative algebra to prove catenarity in generic quantum matrices, and then to show that torus-invariant 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 torus-invariant primes in generic quantum matrices, torus orbits of symplectic leaves in matrix Poisson varieties and totally non-negative cells in totally non-negative 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 non-negative matrices such as new recognition tests [18 Launois, S., Lenagan, T. (2014). E?cient recognition of totally non-negative 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 10.1080/00927872.2016.1175619 Poisson Algebra, Poisson Dixmier–Moeglin equivalence, Poisson spectrum Q Science > QA Mathematics (inc Computing science) Faculties > Sciences > School of Mathematics Statistics and Actuarial Science Stephane Launois 10 Nov 2014 11:19 UTC 29 May 2019 13:25 UTC https://kar.kent.ac.uk/id/eprint/44211 (The current URI for this page, for reference purposes)