# LND-FILTRATIONS AND SEMI-RIGID DOMAINS

Abstract : We investigate the filtration corresponding to the degree function induced by a non-zero locally nilpotent derivation and its associated graded algebra. We show that this kind of filtration, referred to as the LND-filtration, is the ideal candidate to study the structure of semi-rigid k-domains, that is, k-domains for which every non-zero locally nilpotent derivation gives rise to the same filtration. Indeed, the LND-filtration gives a very precise understanding of these structure, it is impeccable for the computation of the Makar-Limanov invariant, and it is an efficient tool to determine their isomorphism types and automorphism groups. Then, we construct a new interesting class of semi-rigid k-domains in which we elaborate the fundamental requirement of LND-filtrations. The importance of these new examples is due to the fact that they possess a relatively big set of invariant sub-algebras, which can not be recoverd by known invariants such as the Makar-Limanov and the Derksen invariants. Also, we define a new family of invariant sub-algebras as a generalization of the Derksen invariant. Finally, we introduce an algorithm to establish explicit isomorphisms between cylinders over non-isomorphic members of the new class, providing by that new counter-examples to the cancellation problem.
Type de document :
Pré-publication, Document de travail
2015

https://hal.archives-ouvertes.fr/hal-01099283
Contributeur : Bachar Alhajjar <>
Soumis le : vendredi 2 janvier 2015 - 13:57:55
Dernière modification le : mardi 12 janvier 2016 - 12:58:01
Document(s) archivé(s) le : vendredi 3 avril 2015 - 10:11:49

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### Identifiants

• HAL Id : hal-01099283, version 1
• ARXIV : 1501.00445

### Citation

Bachar Alhajjar. LND-FILTRATIONS AND SEMI-RIGID DOMAINS. 2015. <hal-01099283>

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