Operator algebras for higher rank analysis and their application to factorial languages
We study strong compactly aligned product systems of ℤ + N over a C*-algebra A . We provide a description of their Cuntz-Nica-Pimsner algebra in terms of tractable relations coming from ideals of A . This approach encompasses product systems where the left action is given by compacts, as well as a w...
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| Veröffentlicht in: | Journal d'analyse mathématique (Jerusalem) 2021-06, Vol.143 (2), p.555-613 |
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| container_title | Journal d'analyse mathématique (Jerusalem) |
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| creator | Dor-On, Adam Kakariadis, Evgenios T. A. |
| description | We study strong compactly aligned product systems of ℤ
+
N
over a C*-algebra
A
. We provide a description of their Cuntz-Nica-Pimsner algebra in terms of tractable relations coming from ideals of
A
. This approach encompasses product systems where the left action is given by compacts, as well as a wide class of higher rank graphs (beyond row-finite).
Moreover we analyze higher rank factorial languages and their C*-algebras. Many of the rank one results in the literature find here their higher rank analogues. In particular, we show that the Cuntz-Nica-Pimsner algebra of a higher rank sofic language coincides with the Cuntz-Krieger algebra of its unlabeled follower set higher rank graph. However, there are also differences. For example, the Cuntz-Nica-Pimsner can lie in-between the first quantization and its quotient by the compactly supported operators. |
| doi_str_mv | 10.1007/s11854-021-0163-6 |
| format | Article |
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+
N
over a C*-algebra
A
. We provide a description of their Cuntz-Nica-Pimsner algebra in terms of tractable relations coming from ideals of
A
. This approach encompasses product systems where the left action is given by compacts, as well as a wide class of higher rank graphs (beyond row-finite).
Moreover we analyze higher rank factorial languages and their C*-algebras. Many of the rank one results in the literature find here their higher rank analogues. In particular, we show that the Cuntz-Nica-Pimsner algebra of a higher rank sofic language coincides with the Cuntz-Krieger algebra of its unlabeled follower set higher rank graph. However, there are also differences. For example, the Cuntz-Nica-Pimsner can lie in-between the first quantization and its quotient by the compactly supported operators.</description><identifier>ISSN: 0021-7670</identifier><identifier>EISSN: 1565-8538</identifier><identifier>DOI: 10.1007/s11854-021-0163-6</identifier><language>eng</language><publisher>Jerusalem: The Hebrew University Magnes Press</publisher><subject>Abstract Harmonic Analysis ; Algebra ; Analysis ; Compacts ; Dynamical Systems and Ergodic Theory ; Functional Analysis ; Languages ; Mathematics ; Mathematics and Statistics ; Operators (mathematics) ; Partial Differential Equations ; Quotients</subject><ispartof>Journal d'analyse mathématique (Jerusalem), 2021-06, Vol.143 (2), p.555-613</ispartof><rights>The Hebrew University of Jerusalem 2021</rights><rights>The Hebrew University of Jerusalem 2021.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c359t-f86cb23d6cef9ea8fbd03bec891061354aa81b752506833aaf14d80025cefabb3</citedby><cites>FETCH-LOGICAL-c359t-f86cb23d6cef9ea8fbd03bec891061354aa81b752506833aaf14d80025cefabb3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11854-021-0163-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11854-021-0163-6$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Dor-On, Adam</creatorcontrib><creatorcontrib>Kakariadis, Evgenios T. A.</creatorcontrib><title>Operator algebras for higher rank analysis and their application to factorial languages</title><title>Journal d'analyse mathématique (Jerusalem)</title><addtitle>JAMA</addtitle><description>We study strong compactly aligned product systems of ℤ
+
N
over a C*-algebra
A
. We provide a description of their Cuntz-Nica-Pimsner algebra in terms of tractable relations coming from ideals of
A
. This approach encompasses product systems where the left action is given by compacts, as well as a wide class of higher rank graphs (beyond row-finite).
Moreover we analyze higher rank factorial languages and their C*-algebras. Many of the rank one results in the literature find here their higher rank analogues. In particular, we show that the Cuntz-Nica-Pimsner algebra of a higher rank sofic language coincides with the Cuntz-Krieger algebra of its unlabeled follower set higher rank graph. However, there are also differences. For example, the Cuntz-Nica-Pimsner can lie in-between the first quantization and its quotient by the compactly supported operators.</description><subject>Abstract Harmonic Analysis</subject><subject>Algebra</subject><subject>Analysis</subject><subject>Compacts</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Functional Analysis</subject><subject>Languages</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators (mathematics)</subject><subject>Partial Differential Equations</subject><subject>Quotients</subject><issn>0021-7670</issn><issn>1565-8538</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LxDAQhoMouK7-AG8Bz9F8bNL0KItfsLAXxWOYpEk3a21r0j34781SwZOnmWHe92XmQeia0VtGaXWXGdNyRShnhDIliDpBCyaVJFoKfYoW9LipVEXP0UXOe0qlrAVfoPft6BNMQ8LQtd4myDiUYRfbnU84Qf-BoYfuO8dcmgZPOx-Ldhy76GCKQ4-nAQdwJSFChzvo2wO0Pl-iswBd9le_dYneHh9e189ks316Wd9viBOynkjQylkuGuV8qD3oYBsqrHe6ZlQxIVcAmtlKckmVFgIgsFWjyzOyGMBasUQ3c-6Yhq-Dz5PZD4dULs6GS0W15KrmRcVmlUtDzskHM6b4CenbMGqO_MzMzxRK5sjPqOLhsycXbd_69Jf8v-kHfx1z9Q</recordid><startdate>20210601</startdate><enddate>20210601</enddate><creator>Dor-On, Adam</creator><creator>Kakariadis, Evgenios T. A.</creator><general>The Hebrew University Magnes Press</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20210601</creationdate><title>Operator algebras for higher rank analysis and their application to factorial languages</title><author>Dor-On, Adam ; Kakariadis, Evgenios T. A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c359t-f86cb23d6cef9ea8fbd03bec891061354aa81b752506833aaf14d80025cefabb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Algebra</topic><topic>Analysis</topic><topic>Compacts</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Functional Analysis</topic><topic>Languages</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operators (mathematics)</topic><topic>Partial Differential Equations</topic><topic>Quotients</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dor-On, Adam</creatorcontrib><creatorcontrib>Kakariadis, Evgenios T. A.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal d'analyse mathématique (Jerusalem)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dor-On, Adam</au><au>Kakariadis, Evgenios T. A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Operator algebras for higher rank analysis and their application to factorial languages</atitle><jtitle>Journal d'analyse mathématique (Jerusalem)</jtitle><stitle>JAMA</stitle><date>2021-06-01</date><risdate>2021</risdate><volume>143</volume><issue>2</issue><spage>555</spage><epage>613</epage><pages>555-613</pages><issn>0021-7670</issn><eissn>1565-8538</eissn><abstract>We study strong compactly aligned product systems of ℤ
+
N
over a C*-algebra
A
. We provide a description of their Cuntz-Nica-Pimsner algebra in terms of tractable relations coming from ideals of
A
. This approach encompasses product systems where the left action is given by compacts, as well as a wide class of higher rank graphs (beyond row-finite).
Moreover we analyze higher rank factorial languages and their C*-algebras. Many of the rank one results in the literature find here their higher rank analogues. In particular, we show that the Cuntz-Nica-Pimsner algebra of a higher rank sofic language coincides with the Cuntz-Krieger algebra of its unlabeled follower set higher rank graph. However, there are also differences. For example, the Cuntz-Nica-Pimsner can lie in-between the first quantization and its quotient by the compactly supported operators.</abstract><cop>Jerusalem</cop><pub>The Hebrew University Magnes Press</pub><doi>10.1007/s11854-021-0163-6</doi><tpages>59</tpages><oa>free_for_read</oa></addata></record> |
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| issn | 0021-7670 1565-8538 |
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| subjects | Abstract Harmonic Analysis Algebra Analysis Compacts Dynamical Systems and Ergodic Theory Functional Analysis Languages Mathematics Mathematics and Statistics Operators (mathematics) Partial Differential Equations Quotients |
| title | Operator algebras for higher rank analysis and their application to factorial languages |
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