caa a22 4500 445862459 CHVBK 20180317145447.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00031-011-9162-5 doi (NATIONALLICENCE)springer-10.1007/s00031-011-9162-5 Bulois M. LAREMA, 2 boulevard Lavoisier, FR-49045, Angers Cedex 1, France aut Irregular locus of the commuting variety of reductive symmetric lie algebras and rigid pairs [Elektronische Daten] [M. Bulois] The aim of this paper is to describe the irregular locus of the commuting variety of a reductive symmetric Lie algebra. More precisely, we want to enlighten a remark of V. L. Popov. In one of his papers, the irregular locus of the commuting variety of any reductive Lie algebra is described and its codimension is computed. This provides a bound for the codimension of the singular locus of this commuting variety. V. L. Popov also suggests that his arguments and methods are suitable for obtaining analogous results in the symmetric setting. We show that some difficulties arise in this case and we obtain some results on the irregular locus of the component of maximal dimension of the "symmetric commuting variety”. As a by-product, we study some pairs of commuting elements specific to the symmetric case, that we call rigid pairs. These pairs allow us to find all symmetric Lie algebras whose commuting variety is reducible. Springer Science+Business Media, LLC, 2011 Transformation Groups SP Birkhäuser Verlag Boston 16/4(2011-12-01), 1027-1061 1083-4362 16:4<1027 2011 16 31 https://doi.org/10.1007/s00031-011-9162-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00031-011-9162-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bulois M. LAREMA, 2 boulevard Lavoisier, FR-49045, Angers Cedex 1, France aut NATIONALLICENCE 773 0- Transformation Groups SP Birkhäuser Verlag Boston 16/4(2011-12-01), 1027-1061 1083-4362 16:4<1027 2011 16 31 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer