Cyclic structures in algebraic (co)homology theories
This note discusses the cyclic cohomology of a left Hopf algebroid (\times_A-Hopf algebra) with coefficients in a right module-left comodule, defined using a straightforward generalisation of the original operators given by Connes and Moscovici for Hopf algebras. Lie-Rinehart homology is a special c...
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| Veröffentlicht in: | Homology, homotopy, and applications homotopy, and applications, 2011, Vol.13 (1), p.297-318 |
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| container_title | Homology, homotopy, and applications |
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| creator | Kowalzig, Niels Krähmer, Ulrich |
| description | This note discusses the cyclic cohomology of a left Hopf algebroid (\times_A-Hopf algebra) with coefficients in a right module-left
comodule, defined using a straightforward generalisation of the
original operators given by Connes and Moscovici for Hopf algebras. Lie-Rinehart homology is a special case of this theory. A
generalisation of cyclic duality that makes sense for arbitrary
para-cyclic objects yields a dual homology theory. The twisted
cyclic homology of an associative algebra provides an example
of this dual theory that uses coefficients that are not necessarily
stable anti Yetter-Drinfel’d modules |
| doi_str_mv | 10.4310/HHA.2011.v13.n1.a12 |
| format | Article |
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comodule, defined using a straightforward generalisation of the
original operators given by Connes and Moscovici for Hopf algebras. Lie-Rinehart homology is a special case of this theory. A
generalisation of cyclic duality that makes sense for arbitrary
para-cyclic objects yields a dual homology theory. The twisted
cyclic homology of an associative algebra provides an example
of this dual theory that uses coefficients that are not necessarily
stable anti Yetter-Drinfel’d modules</description><identifier>ISSN: 1532-0073</identifier><identifier>EISSN: 1532-0081</identifier><identifier>DOI: 10.4310/HHA.2011.v13.n1.a12</identifier><language>eng</language><publisher>International Press of Boston</publisher><subject>16E40 ; 16T05 ; 16T15 ; 19D55 ; 58B34 ; Cyclic homology ; Hopf algebroid ; Lie-Rinehart algebra ; twisted cyclic homology</subject><ispartof>Homology, homotopy, and applications, 2011, Vol.13 (1), p.297-318</ispartof><rights>Copyright 2011 International Press of Boston</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c351t-ed12328ae766c4a7bf5b4ea99138e11d794936bb108644b43824b68b5d492e1d3</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,776,780,881,4010,27900,27901,27902</link.rule.ids></links><search><creatorcontrib>Kowalzig, Niels</creatorcontrib><creatorcontrib>Krähmer, Ulrich</creatorcontrib><title>Cyclic structures in algebraic (co)homology theories</title><title>Homology, homotopy, and applications</title><description>This note discusses the cyclic cohomology of a left Hopf algebroid (\times_A-Hopf algebra) with coefficients in a right module-left
comodule, defined using a straightforward generalisation of the
original operators given by Connes and Moscovici for Hopf algebras. Lie-Rinehart homology is a special case of this theory. A
generalisation of cyclic duality that makes sense for arbitrary
para-cyclic objects yields a dual homology theory. The twisted
cyclic homology of an associative algebra provides an example
of this dual theory that uses coefficients that are not necessarily
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comodule, defined using a straightforward generalisation of the
original operators given by Connes and Moscovici for Hopf algebras. Lie-Rinehart homology is a special case of this theory. A
generalisation of cyclic duality that makes sense for arbitrary
para-cyclic objects yields a dual homology theory. The twisted
cyclic homology of an associative algebra provides an example
of this dual theory that uses coefficients that are not necessarily
stable anti Yetter-Drinfel’d modules</abstract><pub>International Press of Boston</pub><doi>10.4310/HHA.2011.v13.n1.a12</doi><tpages>22</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Homology, homotopy, and applications, 2011, Vol.13 (1), p.297-318 |
| issn | 1532-0073 1532-0081 |
| language | eng |
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| source | International Press Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Alma/SFX Local Collection |
| subjects | 16E40 16T05 16T15 19D55 58B34 Cyclic homology Hopf algebroid Lie-Rinehart algebra twisted cyclic homology |
| title | Cyclic structures in algebraic (co)homology theories |
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