Mid-reversibility properties of semigroup actions on homogeneous spaces
In this paper we study mid-reversibility of subsemigroups acting on homogeneous spaces. The mid-reversor set of a subsemigroup is defined and it is described in terms of the invariant control sets for semigroups acting on certain homogeneous spaces. Let G be a connected noncompact semi-simple Lie gr...
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| Veröffentlicht in: | Semigroup forum 2022-06, Vol.104 (3), p.689-703 |
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| creator | Reis, Ronan A. San Martin, Luiz A. B. Rocha, Victor H. L. |
| description | In this paper we study mid-reversibility of subsemigroups acting on homogeneous spaces. The mid-reversor set of a subsemigroup is defined and it is described in terms of the invariant control sets for semigroups acting on certain homogeneous spaces. Let
G
be a connected noncompact semi-simple Lie group and
L
a subgroup of
G
. Assume that
S
is a subsemigroup of
G
with nonempty interior. We characterize the mid-reversibility of the
S
-action on
G
/
L
in terms of the actions of
S
and
L
on the flag manifolds of
G
. We show that the mid-reversibility of
S
in
G
/
L
is related to the reversibility of
S
in
G
/
L
. We also present sufficient conditions for
S
to generate
G
if
S
is mid-reversible in
G
/
L
. |
| doi_str_mv | 10.1007/s00233-022-10275-5 |
| format | Article |
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G
be a connected noncompact semi-simple Lie group and
L
a subgroup of
G
. Assume that
S
is a subsemigroup of
G
with nonempty interior. We characterize the mid-reversibility of the
S
-action on
G
/
L
in terms of the actions of
S
and
L
on the flag manifolds of
G
. We show that the mid-reversibility of
S
in
G
/
L
is related to the reversibility of
S
in
G
/
L
. We also present sufficient conditions for
S
to generate
G
if
S
is mid-reversible in
G
/
L
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G
be a connected noncompact semi-simple Lie group and
L
a subgroup of
G
. Assume that
S
is a subsemigroup of
G
with nonempty interior. We characterize the mid-reversibility of the
S
-action on
G
/
L
in terms of the actions of
S
and
L
on the flag manifolds of
G
. We show that the mid-reversibility of
S
in
G
/
L
is related to the reversibility of
S
in
G
/
L
. We also present sufficient conditions for
S
to generate
G
if
S
is mid-reversible in
G
/
L
.</description><subject>Algebra</subject><subject>Lie groups</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Research Article</subject><subject>Semigroups</subject><subject>Subgroups</subject><issn>0037-1912</issn><issn>1432-2137</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhoMouH78AU8Fz9HJJOnHURZdhRUveg5pO12z7DY1aYX990YrePMywwzv-87wMHYl4EYAFLcRAKXkgMgFYKG5PmILoSRyFLI4ZgsAWXBRCTxlZzFuIc2QywVbPbuWB_qkEF3tdm48ZEPwA4XRUcx8l0Xau03w05DZZnS-T8s-e_d7v6Ge_BSzONiG4gU76ewu0uVvP2dvD_evy0e-flk9Le_WvEGAMVUtagVF3VadlUTUlm2hc1tS2dWyQVJlgVpWed1Im4MCtJWqsbFtZXORJOfses5NX35MFEez9VPo00mDeSmFRqWqpMJZ1QQfY6DODMHtbTgYAeYbmJmBmQTM_AAzOpnkbIpJ3G8o_EX_4_oCvhtvAQ</recordid><startdate>20220601</startdate><enddate>20220601</enddate><creator>Reis, Ronan A.</creator><creator>San Martin, Luiz A. B.</creator><creator>Rocha, Victor H. L.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20220601</creationdate><title>Mid-reversibility properties of semigroup actions on homogeneous spaces</title><author>Reis, Ronan A. ; San Martin, Luiz A. B. ; Rocha, Victor H. L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-c251b407bd9fa3eeed8d756a8e8fb3c2e48725396bc3a60402a94b2cad9a61fb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Algebra</topic><topic>Lie groups</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Research Article</topic><topic>Semigroups</topic><topic>Subgroups</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Reis, Ronan A.</creatorcontrib><creatorcontrib>San Martin, Luiz A. B.</creatorcontrib><creatorcontrib>Rocha, Victor H. L.</creatorcontrib><collection>CrossRef</collection><jtitle>Semigroup forum</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Reis, Ronan A.</au><au>San Martin, Luiz A. B.</au><au>Rocha, Victor H. L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Mid-reversibility properties of semigroup actions on homogeneous spaces</atitle><jtitle>Semigroup forum</jtitle><stitle>Semigroup Forum</stitle><date>2022-06-01</date><risdate>2022</risdate><volume>104</volume><issue>3</issue><spage>689</spage><epage>703</epage><pages>689-703</pages><issn>0037-1912</issn><eissn>1432-2137</eissn><abstract>In this paper we study mid-reversibility of subsemigroups acting on homogeneous spaces. The mid-reversor set of a subsemigroup is defined and it is described in terms of the invariant control sets for semigroups acting on certain homogeneous spaces. Let
G
be a connected noncompact semi-simple Lie group and
L
a subgroup of
G
. Assume that
S
is a subsemigroup of
G
with nonempty interior. We characterize the mid-reversibility of the
S
-action on
G
/
L
in terms of the actions of
S
and
L
on the flag manifolds of
G
. We show that the mid-reversibility of
S
in
G
/
L
is related to the reversibility of
S
in
G
/
L
. We also present sufficient conditions for
S
to generate
G
if
S
is mid-reversible in
G
/
L
.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00233-022-10275-5</doi><tpages>15</tpages></addata></record> |
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| ispartof | Semigroup forum, 2022-06, Vol.104 (3), p.689-703 |
| issn | 0037-1912 1432-2137 |
| language | eng |
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| subjects | Algebra Lie groups Mathematics Mathematics and Statistics Research Article Semigroups Subgroups |
| title | Mid-reversibility properties of semigroup actions on homogeneous spaces |
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