An Algebraic Analogue of Exel–Pardo C∗-Algebras
We introduce an algebraic version of the Katsura C ∗ -algebra of a pair A , B of integer matrices and an algebraic version of the Exel–Pardo C ∗ -algebra of a self-similar action on a graph. We prove a Graded Uniqueness Theorem for such algebras and construct a homomorphism of the latter into a Stei...
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| Veröffentlicht in: | Algebras and representation theory 2021-08, Vol.24 (4), p.877-909 |
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| container_end_page | 909 |
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| container_title | Algebras and representation theory |
| container_volume | 24 |
| creator | Hazrat, Roozbeh Pask, David Sierakowski, Adam Sims, Aidan |
| description | We introduce an algebraic version of the Katsura
C
∗
-algebra of a pair
A
,
B
of integer matrices and an algebraic version of the Exel–Pardo
C
∗
-algebra of a self-similar action on a graph. We prove a Graded Uniqueness Theorem for such algebras and construct a homomorphism of the latter into a Steinberg algebra that, under mild conditions, is an isomorphism. Working with Steinberg algebras over non-Hausdorff groupoids we prove that in the unital case, our algebraic version of Katsura
C
∗
-algebras are all isomorphic to Steinberg algebras. |
| doi_str_mv | 10.1007/s10468-020-09973-x |
| format | Article |
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C
∗
-algebra of a pair
A
,
B
of integer matrices and an algebraic version of the Exel–Pardo
C
∗
-algebra of a self-similar action on a graph. We prove a Graded Uniqueness Theorem for such algebras and construct a homomorphism of the latter into a Steinberg algebra that, under mild conditions, is an isomorphism. Working with Steinberg algebras over non-Hausdorff groupoids we prove that in the unital case, our algebraic version of Katsura
C
∗
-algebras are all isomorphic to Steinberg algebras.</description><identifier>ISSN: 1386-923X</identifier><identifier>EISSN: 1572-9079</identifier><identifier>DOI: 10.1007/s10468-020-09973-x</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Algebra ; Associative Rings and Algebras ; Commutative Rings and Algebras ; Homomorphisms ; Isomorphism ; Mathematics ; Mathematics and Statistics ; Matrix algebra ; Non-associative Rings and Algebras ; Self-similarity ; Uniqueness theorems</subject><ispartof>Algebras and representation theory, 2021-08, Vol.24 (4), p.877-909</ispartof><rights>Springer Nature B.V. 2020</rights><rights>Springer Nature B.V. 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c234x-65ea6b5215a2f60aeacc983e3cd48cb39dcf97c55c5e3dad01dad3d27df118f33</citedby><cites>FETCH-LOGICAL-c234x-65ea6b5215a2f60aeacc983e3cd48cb39dcf97c55c5e3dad01dad3d27df118f33</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/s10468-020-09973-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10468-020-09973-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Hazrat, Roozbeh</creatorcontrib><creatorcontrib>Pask, David</creatorcontrib><creatorcontrib>Sierakowski, Adam</creatorcontrib><creatorcontrib>Sims, Aidan</creatorcontrib><title>An Algebraic Analogue of Exel–Pardo C∗-Algebras</title><title>Algebras and representation theory</title><addtitle>Algebr Represent Theor</addtitle><description>We introduce an algebraic version of the Katsura
C
∗
-algebra of a pair
A
,
B
of integer matrices and an algebraic version of the Exel–Pardo
C
∗
-algebra of a self-similar action on a graph. We prove a Graded Uniqueness Theorem for such algebras and construct a homomorphism of the latter into a Steinberg algebra that, under mild conditions, is an isomorphism. Working with Steinberg algebras over non-Hausdorff groupoids we prove that in the unital case, our algebraic version of Katsura
C
∗
-algebras are all isomorphic to Steinberg algebras.</description><subject>Algebra</subject><subject>Associative Rings and Algebras</subject><subject>Commutative Rings and Algebras</subject><subject>Homomorphisms</subject><subject>Isomorphism</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Matrix algebra</subject><subject>Non-associative Rings and Algebras</subject><subject>Self-similarity</subject><subject>Uniqueness theorems</subject><issn>1386-923X</issn><issn>1572-9079</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kD1PwzAQhi0EEqXwB5giMRvOvjiOx6gqH1IlGEBisxx_VK1CU2wqhY2RnYH_119CSiqxsdzd8LyvTg8h5wwuGYC8SgzyoqTAgYJSEml3QEZMSE4VSHXY31gWVHF8PiYnKS0BQBUlGxGsVlnVzH0dzcJm1co07XzjszZk084324-vBxNdm022n990z6VTchRMk_zZfo_J0_X0cXJLZ_c3d5NqRi3HvKOF8KaoBWfC8FCA8cZaVaJH6_LS1qicDUpaIazw6IwD1g90XLrAWBkQx-Ri6F3H9nXj05tetpvYv5g0F7mSoEDsKD5QNrYpRR_0Oi5eTHzXDPROjh7k6F6O_pWjuz6EQyj18Gru41_1P6kfdTBpCg</recordid><startdate>20210801</startdate><enddate>20210801</enddate><creator>Hazrat, Roozbeh</creator><creator>Pask, David</creator><creator>Sierakowski, Adam</creator><creator>Sims, Aidan</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20210801</creationdate><title>An Algebraic Analogue of Exel–Pardo C∗-Algebras</title><author>Hazrat, Roozbeh ; Pask, David ; Sierakowski, Adam ; Sims, Aidan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c234x-65ea6b5215a2f60aeacc983e3cd48cb39dcf97c55c5e3dad01dad3d27df118f33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Algebra</topic><topic>Associative Rings and Algebras</topic><topic>Commutative Rings and Algebras</topic><topic>Homomorphisms</topic><topic>Isomorphism</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Matrix algebra</topic><topic>Non-associative Rings and Algebras</topic><topic>Self-similarity</topic><topic>Uniqueness theorems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hazrat, Roozbeh</creatorcontrib><creatorcontrib>Pask, David</creatorcontrib><creatorcontrib>Sierakowski, Adam</creatorcontrib><creatorcontrib>Sims, Aidan</creatorcontrib><collection>CrossRef</collection><jtitle>Algebras and representation theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hazrat, Roozbeh</au><au>Pask, David</au><au>Sierakowski, Adam</au><au>Sims, Aidan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An Algebraic Analogue of Exel–Pardo C∗-Algebras</atitle><jtitle>Algebras and representation theory</jtitle><stitle>Algebr Represent Theor</stitle><date>2021-08-01</date><risdate>2021</risdate><volume>24</volume><issue>4</issue><spage>877</spage><epage>909</epage><pages>877-909</pages><issn>1386-923X</issn><eissn>1572-9079</eissn><abstract>We introduce an algebraic version of the Katsura
C
∗
-algebra of a pair
A
,
B
of integer matrices and an algebraic version of the Exel–Pardo
C
∗
-algebra of a self-similar action on a graph. We prove a Graded Uniqueness Theorem for such algebras and construct a homomorphism of the latter into a Steinberg algebra that, under mild conditions, is an isomorphism. Working with Steinberg algebras over non-Hausdorff groupoids we prove that in the unital case, our algebraic version of Katsura
C
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| fulltext | fulltext |
| identifier | ISSN: 1386-923X |
| ispartof | Algebras and representation theory, 2021-08, Vol.24 (4), p.877-909 |
| issn | 1386-923X 1572-9079 |
| language | eng |
| recordid | cdi_proquest_journals_2549709053 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Algebra Associative Rings and Algebras Commutative Rings and Algebras Homomorphisms Isomorphism Mathematics Mathematics and Statistics Matrix algebra Non-associative Rings and Algebras Self-similarity Uniqueness theorems |
| title | An Algebraic Analogue of Exel–Pardo C∗-Algebras |
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