No Cover Image

Journal article 909 views 62 downloads

Circle and Line Bundles Over Generalized Weyl Algebras

Tomasz Brzeziński, Tomasz Brzezinski Orcid Logo

Algebras and Representation Theory, Volume: 19, Issue: 1, Pages: 57 - 69

Swansea University Author: Tomasz Brzezinski Orcid Logo

Abstract

Strongly Z-graded algebras or principal circle bundles and associated line bundles or invertible bimodules over a class of generalized Weyl algebras B(p;q,0) (over a ring of polynomials in one variable) are constructed. The Chern-Connes pairing between the cyclic cohomology of B(p;q,0) and the isomo...

Full description

Published in: Algebras and Representation Theory
ISSN: 1386-923X 1572-9079
Published: 2016
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa22634
Tags: Add Tag
No Tags, Be the first to tag this record!
first_indexed 2015-07-23T02:04:17Z
last_indexed 2018-07-30T12:56:57Z
id cronfa22634
recordtype SURis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2018-07-30T10:01:45.2569910</datestamp><bib-version>v2</bib-version><id>22634</id><entry>2015-07-22</entry><title>Circle and Line Bundles Over Generalized Weyl Algebras</title><swanseaauthors><author><sid>30466d840b59627325596fbbb2c82754</sid><ORCID>0000-0001-6270-3439</ORCID><firstname>Tomasz</firstname><surname>Brzezinski</surname><name>Tomasz Brzezinski</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2015-07-22</date><deptcode>SMA</deptcode><abstract>Strongly Z-graded algebras or principal circle bundles and associated line bundles or invertible bimodules over a class of generalized Weyl algebras B(p;q,0) (over a ring of polynomials in one variable) are constructed. The Chern-Connes pairing between the cyclic cohomology of B(p;q,0) and the isomorphism classes of sections of associated line bundles over B(p;q,0) is computed, thus demonstrating that these bundles, which are labelled by integers, are non-trivial and mutually non- isomorphic. The constructed strongly Z-graded algebras are shown to have Hochschild cohomology reminiscent of that of Calabi-Yau algebras. The paper is supplemented by an observation that a grading by an Abelian group in the middle of a short exact sequence is strong if and only if the induced gradings by the outer groups in the sequence are strong.</abstract><type>Journal Article</type><journal>Algebras and Representation Theory</journal><volume>19</volume><journalNumber>1</journalNumber><paginationStart>57</paginationStart><paginationEnd>69</paginationEnd><publisher/><issnPrint>1386-923X</issnPrint><issnElectronic>1572-9079</issnElectronic><keywords/><publishedDay>31</publishedDay><publishedMonth>12</publishedMonth><publishedYear>2016</publishedYear><publishedDate>2016-12-31</publishedDate><doi>10.1007/s10468-015-9562-7</doi><url/><notes></notes><college>COLLEGE NANME</college><department>Mathematics</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>SMA</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2018-07-30T10:01:45.2569910</lastEdited><Created>2015-07-22T09:10:26.7005454</Created><path><level id="1">College of Science</level><level id="2">Mathematics</level></path><authors><author><firstname>Tomasz</firstname><surname>Brzezi&#x144;ski</surname><order>1</order></author><author><firstname>Tomasz</firstname><surname>Brzezinski</surname><orcid>0000-0001-6270-3439</orcid><order>2</order></author></authors><documents><document><filename>0022634-01052018145427.pdf</filename><originalFilename>Weyl_rev-corr.pdf</originalFilename><uploaded>2018-05-01T14:54:27.5970000</uploaded><type>Output</type><contentLength>319498</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2018-05-01T00:00:00.0000000</embargoDate><copyrightCorrect>true</copyrightCorrect><language>eng</language></document></documents><OutputDurs/></rfc1807>
spelling 2018-07-30T10:01:45.2569910 v2 22634 2015-07-22 Circle and Line Bundles Over Generalized Weyl Algebras 30466d840b59627325596fbbb2c82754 0000-0001-6270-3439 Tomasz Brzezinski Tomasz Brzezinski true false 2015-07-22 SMA Strongly Z-graded algebras or principal circle bundles and associated line bundles or invertible bimodules over a class of generalized Weyl algebras B(p;q,0) (over a ring of polynomials in one variable) are constructed. The Chern-Connes pairing between the cyclic cohomology of B(p;q,0) and the isomorphism classes of sections of associated line bundles over B(p;q,0) is computed, thus demonstrating that these bundles, which are labelled by integers, are non-trivial and mutually non- isomorphic. The constructed strongly Z-graded algebras are shown to have Hochschild cohomology reminiscent of that of Calabi-Yau algebras. The paper is supplemented by an observation that a grading by an Abelian group in the middle of a short exact sequence is strong if and only if the induced gradings by the outer groups in the sequence are strong. Journal Article Algebras and Representation Theory 19 1 57 69 1386-923X 1572-9079 31 12 2016 2016-12-31 10.1007/s10468-015-9562-7 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2018-07-30T10:01:45.2569910 2015-07-22T09:10:26.7005454 College of Science Mathematics Tomasz Brzeziński 1 Tomasz Brzezinski 0000-0001-6270-3439 2 0022634-01052018145427.pdf Weyl_rev-corr.pdf 2018-05-01T14:54:27.5970000 Output 319498 application/pdf Accepted Manuscript true 2018-05-01T00:00:00.0000000 true eng
title Circle and Line Bundles Over Generalized Weyl Algebras
spellingShingle Circle and Line Bundles Over Generalized Weyl Algebras
Tomasz Brzezinski
title_short Circle and Line Bundles Over Generalized Weyl Algebras
title_full Circle and Line Bundles Over Generalized Weyl Algebras
title_fullStr Circle and Line Bundles Over Generalized Weyl Algebras
title_full_unstemmed Circle and Line Bundles Over Generalized Weyl Algebras
title_sort Circle and Line Bundles Over Generalized Weyl Algebras
author_id_str_mv 30466d840b59627325596fbbb2c82754
author_id_fullname_str_mv 30466d840b59627325596fbbb2c82754_***_Tomasz Brzezinski
author Tomasz Brzezinski
author2 Tomasz Brzeziński
Tomasz Brzezinski
format Journal article
container_title Algebras and Representation Theory
container_volume 19
container_issue 1
container_start_page 57
publishDate 2016
institution Swansea University
issn 1386-923X
1572-9079
doi_str_mv 10.1007/s10468-015-9562-7
college_str College of Science
hierarchytype
hierarchy_top_id collegeofscience
hierarchy_top_title College of Science
hierarchy_parent_id collegeofscience
hierarchy_parent_title College of Science
department_str Mathematics{{{_:::_}}}College of Science{{{_:::_}}}Mathematics
document_store_str 1
active_str 0
description Strongly Z-graded algebras or principal circle bundles and associated line bundles or invertible bimodules over a class of generalized Weyl algebras B(p;q,0) (over a ring of polynomials in one variable) are constructed. The Chern-Connes pairing between the cyclic cohomology of B(p;q,0) and the isomorphism classes of sections of associated line bundles over B(p;q,0) is computed, thus demonstrating that these bundles, which are labelled by integers, are non-trivial and mutually non- isomorphic. The constructed strongly Z-graded algebras are shown to have Hochschild cohomology reminiscent of that of Calabi-Yau algebras. The paper is supplemented by an observation that a grading by an Abelian group in the middle of a short exact sequence is strong if and only if the induced gradings by the outer groups in the sequence are strong.
published_date 2016-12-31T03:33:05Z
_version_ 1737025268560691200
score 10.898123