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Finite groups generated in low real codimension
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0001-6306-6777
2019 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 570, p. 245-281Article in journal (Refereed) Published
Abstract [en]

We study the intersection lattice of the arrangement A G of subspaces fixed by subgroups of a finite linear group G. When G is a reflection group, this arrangement is precisely the hyperplane reflection arrangement of G. We generalize the notion of finite reflection groups. We say that a group G is generated (resp. strictly generated) in codimension k if it is generated by its elements that fix point-wise a subspace of codimension at most k (resp. precisely k). We prove that the alternating subgroup Alt(W) of a reflection group W is strictly generated in codimension two. Further, we compute the intersection lattice of all finite subgroups of GL 3 (R), and moreover, we emphasize the groups that are “minimally generated in real codimension two”, i.e., groups that are strictly generated in codimension two but have no real reflection representations. We also provide several examples of groups generated in higher codimension.

Place, publisher, year, edition, pages
Elsevier, 2019. Vol. 570, p. 245-281
Keywords [en]
Coxter groups, Goups generated in higher codimension, Groups generated in codimension two, Reflection groups, Subspace arrangements
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-246411DOI: 10.1016/j.laa.2019.01.004ISI: 000462811200010Scopus ID: 2-s2.0-85061693712OAI: oai:DiVA.org:kth-246411DiVA, id: diva2:1300888
Note

QC 20190401

Available from: 2019-04-01 Created: 2019-04-01 Last updated: 2019-04-29Bibliographically approved

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Martino, Ivan

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