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Linear Dynamical Systems of Nilpotent Lie Groups
We study the topology of orbits of dynamical systems defined by finite-dimensional representations of nilpotent Lie groups. Thus, the following dichotomy is established: either the interior of the set of regular points is dense in the representation space, or the complement of the set of regular poi...
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| Published in: | The Journal of fourier analysis and applications 2021-10, Vol.27 (5), Article 74 |
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| container_title | The Journal of fourier analysis and applications |
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| creator | Beltita, Ingrid Beltita, Daniel |
| description | We study the topology of orbits of dynamical systems defined by finite-dimensional representations of nilpotent Lie groups. Thus, the following dichotomy is established: either the interior of the set of regular points is dense in the representation space, or the complement of the set of regular points is dense, and then the interior of that complement is either empty or dense in the representation space. The regular points are by definition the points whose orbits are locally compact in their relative topology. We thus generalize some results from the recent literature on linear actions of abelian Lie groups. As an application, we determine the generalized
a
x
+
b
-groups whose
C
∗
-algebras are antiliminary, that is, no closed 2-sided ideal is type I. |
| doi_str_mv | 10.1007/s00041-021-09882-7 |
| format | article |
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a
x
+
b
-groups whose
C
∗
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a
x
+
b
-groups whose
C
∗
-algebras are antiliminary, that is, no closed 2-sided ideal is type I.</description><subject>Abstract Harmonic Analysis</subject><subject>Algebra</subject><subject>Approximations and Expansions</subject><subject>Dynamical systems</subject><subject>Fourier Analysis</subject><subject>Group theory</subject><subject>Lie groups</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Orbits</subject><subject>Partial Differential Equations</subject><subject>Representations</subject><subject>Signal,Image and Speech Processing</subject><subject>Topology</subject><issn>1069-5869</issn><issn>1531-5851</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLAzEUhYMoWKt_wNWA66l5zOSxLFWrMOhCXYd0elNSpsmYzCz6700dwZ2ESw6X893kHoRuCV4QjMV9whhXpMQ0l5KSluIMzUjNSFnLmpxnjbnKmqtLdJXSHmcnE2yGcOM8mFg8HL05uNZ0xfsxDXBIRbDFq-v6MIAfisZBsY5h7NM1urCmS3Dze8_R59Pjx-q5bN7WL6tlU7aslkNplKKGbCSvKk6ZNUCwgK21gghJpdngVrZmY3jNOOPSVExQi5Wy29znrAY2R3fT3D6GrxHSoPdhjD4_qWnNKa0UZyS7FpNrZzrQztswRNPms4W8TfBgXe4vBZEV4VKeADoBbQwpRbC6j-5g4lETrE9R6ilKnQPSP1FqkSE2QSmb_Q7i31_-ob4BAPt0gg</recordid><startdate>20211001</startdate><enddate>20211001</enddate><creator>Beltita, Ingrid</creator><creator>Beltita, Daniel</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-4912-7259</orcidid><orcidid>https://orcid.org/0000-0003-2414-8176</orcidid></search><sort><creationdate>20211001</creationdate><title>Linear Dynamical Systems of Nilpotent Lie Groups</title><author>Beltita, Ingrid ; Beltita, Daniel</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c358t-a992a1b8644623fae107edff717828ab0c8caba6536368a4372f099fdc8c635e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Algebra</topic><topic>Approximations and Expansions</topic><topic>Dynamical systems</topic><topic>Fourier Analysis</topic><topic>Group theory</topic><topic>Lie groups</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Orbits</topic><topic>Partial Differential Equations</topic><topic>Representations</topic><topic>Signal,Image and Speech Processing</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Beltita, Ingrid</creatorcontrib><creatorcontrib>Beltita, Daniel</creatorcontrib><collection>CrossRef</collection><jtitle>The Journal of fourier analysis and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Beltita, Ingrid</au><au>Beltita, Daniel</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Linear Dynamical Systems of Nilpotent Lie Groups</atitle><jtitle>The Journal of fourier analysis and applications</jtitle><stitle>J Fourier Anal Appl</stitle><date>2021-10-01</date><risdate>2021</risdate><volume>27</volume><issue>5</issue><artnum>74</artnum><issn>1069-5869</issn><eissn>1531-5851</eissn><abstract>We study the topology of orbits of dynamical systems defined by finite-dimensional representations of nilpotent Lie groups. Thus, the following dichotomy is established: either the interior of the set of regular points is dense in the representation space, or the complement of the set of regular points is dense, and then the interior of that complement is either empty or dense in the representation space. The regular points are by definition the points whose orbits are locally compact in their relative topology. We thus generalize some results from the recent literature on linear actions of abelian Lie groups. As an application, we determine the generalized
a
x
+
b
-groups whose
C
∗
-algebras are antiliminary, that is, no closed 2-sided ideal is type I.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00041-021-09882-7</doi><orcidid>https://orcid.org/0000-0003-4912-7259</orcidid><orcidid>https://orcid.org/0000-0003-2414-8176</orcidid></addata></record> |
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| ispartof | The Journal of fourier analysis and applications, 2021-10, Vol.27 (5), Article 74 |
| issn | 1069-5869 1531-5851 |
| language | eng |
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| source | Springer Nature |
| subjects | Abstract Harmonic Analysis Algebra Approximations and Expansions Dynamical systems Fourier Analysis Group theory Lie groups Mathematical Methods in Physics Mathematics Mathematics and Statistics Orbits Partial Differential Equations Representations Signal,Image and Speech Processing Topology |
| title | Linear Dynamical Systems of Nilpotent Lie Groups |
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