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.
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Contributor : Bachar Alhajjar <>
Submitted on : Friday, January 2, 2015 - 1:57:55 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
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  • HAL Id : hal-01099283, version 1
  • ARXIV : 1501.00445

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Bachar Alhajjar. LND-FILTRATIONS AND SEMI-RIGID DOMAINS. 2015. ⟨hal-01099283⟩

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