Polar representations of compact groups and convex hulls of their orbits
Publication type: Journal Article
Publication date: 2010-10-01
scimago Q2
wos Q2
SJR: 0.504
CiteScore: 1.3
Impact factor: 0.7
ISSN: 09262245, 18726984
Computational Theory and Mathematics
Analysis
Geometry and Topology
Abstract
The paper contains a characterization of compact groups $G\subseteq\GL(V)$, where $V$ is a finite dimensional real vector space, which have the following property \SP{}: the family of convex hulls of $G$-orbits is a semigroup with respect to the Minkowski addition. If $G$ is finite, then \SP{} holds if and only if $G$ is a Coxeter group; if $G$ is connected then \SP{} is true if and only if $G$ is polar. In general, $G$ satisfies \SP{} if and only if it is polar and its Weyl group is a Coxeter group.
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Total citations:
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Citations from 2024:
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(14.29%)
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GOST
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Gichev V. M. Polar representations of compact groups and convex hulls of their orbits // Differential Geometry and its Applications. 2010. Vol. 28. No. 5. pp. 608-614.
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Gichev V. M. Polar representations of compact groups and convex hulls of their orbits // Differential Geometry and its Applications. 2010. Vol. 28. No. 5. pp. 608-614.
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RIS
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TY - JOUR
DO - 10.1016/j.difgeo.2010.05.005
UR - https://doi.org/10.1016/j.difgeo.2010.05.005
TI - Polar representations of compact groups and convex hulls of their orbits
T2 - Differential Geometry and its Applications
AU - Gichev, V M
PY - 2010
DA - 2010/10/01
PB - Elsevier
SP - 608-614
IS - 5
VL - 28
SN - 0926-2245
SN - 1872-6984
ER -
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BibTex (up to 50 authors)
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@article{2010_Gichev,
author = {V M Gichev},
title = {Polar representations of compact groups and convex hulls of their orbits},
journal = {Differential Geometry and its Applications},
year = {2010},
volume = {28},
publisher = {Elsevier},
month = {oct},
url = {https://doi.org/10.1016/j.difgeo.2010.05.005},
number = {5},
pages = {608--614},
doi = {10.1016/j.difgeo.2010.05.005}
}
Cite this
MLA
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Gichev, V. M.. “Polar representations of compact groups and convex hulls of their orbits.” Differential Geometry and its Applications, vol. 28, no. 5, Oct. 2010, pp. 608-614. https://doi.org/10.1016/j.difgeo.2010.05.005.