1Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, U.S.A. 2Department of Mathematics and Statistics, University of Nevada, Reno, NV 89557, U.S.A.
Journal of Lie Theory, Tome 30 (2020) no. 2, pp. 361-370
We give a simple formula for sectional curvatures on the general linear group, which is also valid for many other matrix groups. Similar formula is given for a reductive Lie group. We also discuss the relation between commuting matrices and zero sectional curvature.
Classification :
53B20, 14L35, 51N30
Mots-clés :
Curvature, general linear group, reductive Lie group, closed subgroup
Affiliations des auteurs :
Luyining Gan
1
;
Ming Liao
1
;
Tin-Yau Tam
2
1
Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, U.S.A.
2
Department of Mathematics and Statistics, University of Nevada, Reno, NV 89557, U.S.A.
Luyining Gan; Ming Liao; Tin-Yau Tam. Curvature of Matrix and Reductive Lie Groups. Journal of Lie Theory, Tome 30 (2020) no. 2, pp. 361-370. http://geodesic.mathdoc.fr/item/JOLT_2020_30_2_a4/
@article{JOLT_2020_30_2_a4,
author = {Luyining Gan and Ming Liao and Tin-Yau Tam},
title = {Curvature of {Matrix} and {Reductive} {Lie} {Groups}},
journal = {Journal of Lie Theory},
pages = {361--370},
year = {2020},
volume = {30},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2020_30_2_a4/}
}
TY - JOUR
AU - Luyining Gan
AU - Ming Liao
AU - Tin-Yau Tam
TI - Curvature of Matrix and Reductive Lie Groups
JO - Journal of Lie Theory
PY - 2020
SP - 361
EP - 370
VL - 30
IS - 2
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%P 361-370
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