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Hilbert series of modules over Lie algebroids
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences.ORCID iD: 0000-0002-8508-878X
Stockholms universitet.
2015 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 432, 129-184 p.Article in journal (Refereed) Published
Abstract [en]

We consider modules M over Lie algebroids gA which are of finite type over a local noetherian ring A. Using ideals J ⊂ A such that gA ·J ⊂ J and the length ℓgA (M/JM) < ∞ we can define in a natural way the Hilbert series of M with respect to the defining ideal J. This notion is in particular studied for modules over the Lie algebroid of k-linear derivations gA = TA(I) that preserve an ideal I ⊂ A, for example when A = On, the ring of convergent power series. Hilbert series over Stanley-Reisner rings are also considered.

Place, publisher, year, edition, pages
2015. Vol. 432, 129-184 p.
Keyword [en]
Lie algebroids, Local systems, Representations of Lie algebras, Hilbert series, Stanley–Reisner rings, Complex analytic singularities
National Category
Geometry Algebra and Logic
Identifiers
URN: urn:nbn:se:hig:diva-19157DOI: 10.1016/j.jalgebra.2015.02.020ISI: 000354001500007Scopus ID: 2-s2.0-84925434959OAI: oai:DiVA.org:hig-19157DiVA: diva2:799992
Available from: 2015-04-01 Created: 2015-04-01 Last updated: 2017-12-04Bibliographically approved

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