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Degree bounds for separating invariants

Kraft, Hanspeter and Kohls, Martin. (2010) Degree bounds for separating invariants. Mathematical research letters, Vol. 17. pp. 1171-1182.

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Official URL: http://edoc.unibas.ch/dok/A5839980

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Abstract

If V is a representation of a linear algebraic group G, a set S of G-invariant regular functions on V is called separating if the following holds: If two elements v,v' from V can be separated by an invariant function, then there is an f from S such that f(v) is different from f(v'). It is known that there always exist finite separating sets. Moreover, if the group G is finite, then the invariant functions of degree ≤ |G| form a separating set. We show that for a non-finite linear algebraic group G such an upper bound for the degrees of a separating set does not exist. If G is finite, we define b(G) to be the minimal number d such that for every G-module V there is a separating set of degree less or equal to d. We show that for a subgroup H of G we have b(H) ≤ b(G) ≤ [G:H] b(H), and that b(G) ≤ b(G/H) b(H) in case H is normal. Moreover, we calculate b(G) for some specific finite groups.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Algebra (Kraft)
UniBasel Contributors:Kraft, Hanspeter
Item Type:Article, refereed
Article Subtype:Research Article
Bibsysno:Link to catalogue
Publisher:International Press
ISSN:1073-2780
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Last Modified:31 Dec 2015 10:49
Deposited On:08 Jun 2012 06:48

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