On the $K$ -theory of $C^{\ast }$ -algebras arising from integral dynamics
We investigate the $K$ -theory of unital UCT Kirchberg algebras ${\mathcal{Q}}_{S}$ arising from families $S$ of relatively prime numbers. It is shown that $K_{\ast }({\mathcal{Q}}_{S})$ is the direct sum of a free abelian group and a torsion group, each of which is realized by another distinct $C^{...
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Veröffentlicht in: | Ergodic theory and dynamical systems 2018-05, Vol.38 (3), p.832-862 |
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creator | BARLAK, SELÇUK OMLAND, TRON STAMMEIER, NICOLAI |
description | We investigate the
$K$
-theory of unital UCT Kirchberg algebras
${\mathcal{Q}}_{S}$
arising from families
$S$
of relatively prime numbers. It is shown that
$K_{\ast }({\mathcal{Q}}_{S})$
is the direct sum of a free abelian group and a torsion group, each of which is realized by another distinct
$C^{\ast }$
-algebra naturally associated to
$S$
. The
$C^{\ast }$
-algebra representing the torsion part is identified with a natural subalgebra
${\mathcal{A}}_{S}$
of
${\mathcal{Q}}_{S}$
. For the
$K$
-theory of
${\mathcal{Q}}_{S}$
, the cardinality of
$S$
determines the free part and is also relevant for the torsion part, for which the greatest common divisor
$g_{S}$
of
$\{p-1:p\in S\}$
plays a central role as well. In the case where
$|S|\leq 2$
or
$g_{S}=1$
we obtain a complete classification for
${\mathcal{Q}}_{S}$
. Our results support the conjecture that
${\mathcal{A}}_{S}$
coincides with
$\otimes _{p\in S}{\mathcal{O}}_{p}$
. This would lead to a complete classification of
${\mathcal{Q}}_{S}$
, and is related to a conjecture about
$k$
-graphs. |
doi_str_mv | 10.1017/etds.2016.63 |
format | Article |
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$K$
-theory of unital UCT Kirchberg algebras
${\mathcal{Q}}_{S}$
arising from families
$S$
of relatively prime numbers. It is shown that
$K_{\ast }({\mathcal{Q}}_{S})$
is the direct sum of a free abelian group and a torsion group, each of which is realized by another distinct
$C^{\ast }$
-algebra naturally associated to
$S$
. The
$C^{\ast }$
-algebra representing the torsion part is identified with a natural subalgebra
${\mathcal{A}}_{S}$
of
${\mathcal{Q}}_{S}$
. For the
$K$
-theory of
${\mathcal{Q}}_{S}$
, the cardinality of
$S$
determines the free part and is also relevant for the torsion part, for which the greatest common divisor
$g_{S}$
of
$\{p-1:p\in S\}$
plays a central role as well. In the case where
$|S|\leq 2$
or
$g_{S}=1$
we obtain a complete classification for
${\mathcal{Q}}_{S}$
. Our results support the conjecture that
${\mathcal{A}}_{S}$
coincides with
$\otimes _{p\in S}{\mathcal{O}}_{p}$
. This would lead to a complete classification of
${\mathcal{Q}}_{S}$
, and is related to a conjecture about
$k$
-graphs.</description><identifier>ISSN: 0143-3857</identifier><identifier>EISSN: 1469-4417</identifier><identifier>DOI: 10.1017/etds.2016.63</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Algebra ; Classification ; Original Article ; Prime numbers ; Torsion</subject><ispartof>Ergodic theory and dynamical systems, 2018-05, Vol.38 (3), p.832-862</ispartof><rights>Cambridge University Press, 2016</rights><rights>info:eu-repo/semantics/openAccess</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S0143385716000638/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>164,230,314,778,782,883,26550,27907,27908,55611</link.rule.ids></links><search><creatorcontrib>BARLAK, SELÇUK</creatorcontrib><creatorcontrib>OMLAND, TRON</creatorcontrib><creatorcontrib>STAMMEIER, NICOLAI</creatorcontrib><title>On the $K$ -theory of $C^{\ast }$ -algebras arising from integral dynamics</title><title>Ergodic theory and dynamical systems</title><addtitle>Ergod. Th. Dynam. Sys</addtitle><description>We investigate the
$K$
-theory of unital UCT Kirchberg algebras
${\mathcal{Q}}_{S}$
arising from families
$S$
of relatively prime numbers. It is shown that
$K_{\ast }({\mathcal{Q}}_{S})$
is the direct sum of a free abelian group and a torsion group, each of which is realized by another distinct
$C^{\ast }$
-algebra naturally associated to
$S$
. The
$C^{\ast }$
-algebra representing the torsion part is identified with a natural subalgebra
${\mathcal{A}}_{S}$
of
${\mathcal{Q}}_{S}$
. For the
$K$
-theory of
${\mathcal{Q}}_{S}$
, the cardinality of
$S$
determines the free part and is also relevant for the torsion part, for which the greatest common divisor
$g_{S}$
of
$\{p-1:p\in S\}$
plays a central role as well. In the case where
$|S|\leq 2$
or
$g_{S}=1$
we obtain a complete classification for
${\mathcal{Q}}_{S}$
. Our results support the conjecture that
${\mathcal{A}}_{S}$
coincides with
$\otimes _{p\in S}{\mathcal{O}}_{p}$
. This would lead to a complete classification of
${\mathcal{Q}}_{S}$
, and is related to a conjecture about
$k$
-graphs.</description><subject>Algebra</subject><subject>Classification</subject><subject>Original Article</subject><subject>Prime numbers</subject><subject>Torsion</subject><issn>0143-3857</issn><issn>1469-4417</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>3HK</sourceid><recordid>eNpFkEtLw0AUhQdRsFZ37h2w28S580qylOK70I3uxGEyuRNT0kRn0kUR_7spLbi6l8PH4fARcgksBQbZDQ5VTDkDnWpxRCYgdZFICdkxmTCQIhG5yk7JWYwrxpiATE3I87KjwyfS2cuMJuPThy3tPZ3NP37ebRzo7xjbtsYy2EhtaGLT1dSHfk2bbsA62JZW286uGxfPyYm3bcSLw52St_u71_ljslg-PM1vF4njUg8JtyXTiExYl1koQHCvvMaiGrMcCpTCO4sakFcCQDqHovIoy9LnyitXiCm52ve6cc7QdKbrgzXAcsWNUqDZSFzvia_Qf28wDmbVb0I3jjKccVFwKRmMVHrosesyNFWN_xgwszNqdkbNzqjRQvwBUZNnIg</recordid><startdate>20180501</startdate><enddate>20180501</enddate><creator>BARLAK, SELÇUK</creator><creator>OMLAND, TRON</creator><creator>STAMMEIER, NICOLAI</creator><general>Cambridge University Press</general><scope>3V.</scope><scope>7SC</scope><scope>7U5</scope><scope>7XB</scope><scope>88I</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>H8D</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M2P</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope><scope>3HK</scope></search><sort><creationdate>20180501</creationdate><title>On the $K$ -theory of $C^{\ast }$ -algebras arising from integral dynamics</title><author>BARLAK, SELÇUK ; OMLAND, TRON ; STAMMEIER, NICOLAI</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c246t-2ab06ee03ac7a19132f5f6e9dee0819e43fcae61e2d3114cce3dfe4bbf85f5c93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Algebra</topic><topic>Classification</topic><topic>Original Article</topic><topic>Prime numbers</topic><topic>Torsion</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>BARLAK, SELÇUK</creatorcontrib><creatorcontrib>OMLAND, TRON</creatorcontrib><creatorcontrib>STAMMEIER, NICOLAI</creatorcontrib><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>Aerospace Database</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><collection>NORA - Norwegian Open Research Archives</collection><jtitle>Ergodic theory and dynamical systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>BARLAK, SELÇUK</au><au>OMLAND, TRON</au><au>STAMMEIER, NICOLAI</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the $K$ -theory of $C^{\ast }$ -algebras arising from integral dynamics</atitle><jtitle>Ergodic theory and dynamical systems</jtitle><addtitle>Ergod. Th. Dynam. Sys</addtitle><date>2018-05-01</date><risdate>2018</risdate><volume>38</volume><issue>3</issue><spage>832</spage><epage>862</epage><pages>832-862</pages><issn>0143-3857</issn><eissn>1469-4417</eissn><abstract>We investigate the
$K$
-theory of unital UCT Kirchberg algebras
${\mathcal{Q}}_{S}$
arising from families
$S$
of relatively prime numbers. It is shown that
$K_{\ast }({\mathcal{Q}}_{S})$
is the direct sum of a free abelian group and a torsion group, each of which is realized by another distinct
$C^{\ast }$
-algebra naturally associated to
$S$
. The
$C^{\ast }$
-algebra representing the torsion part is identified with a natural subalgebra
${\mathcal{A}}_{S}$
of
${\mathcal{Q}}_{S}$
. For the
$K$
-theory of
${\mathcal{Q}}_{S}$
, the cardinality of
$S$
determines the free part and is also relevant for the torsion part, for which the greatest common divisor
$g_{S}$
of
$\{p-1:p\in S\}$
plays a central role as well. In the case where
$|S|\leq 2$
or
$g_{S}=1$
we obtain a complete classification for
${\mathcal{Q}}_{S}$
. Our results support the conjecture that
${\mathcal{A}}_{S}$
coincides with
$\otimes _{p\in S}{\mathcal{O}}_{p}$
. This would lead to a complete classification of
${\mathcal{Q}}_{S}$
, and is related to a conjecture about
$k$
-graphs.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/etds.2016.63</doi><tpages>31</tpages><oa>free_for_read</oa></addata></record> |
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language | eng |
recordid | cdi_cristin_nora_10852_55160 |
source | NORA - Norwegian Open Research Archives; Cambridge Journals |
subjects | Algebra Classification Original Article Prime numbers Torsion |
title | On the $K$ -theory of $C^{\ast }$ -algebras arising from integral dynamics |
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