On Frobenius and separable Galois cowreaths
We show that a Galois cowreath ( A , X ) in a monoidal category C is Frobenius if and only if the subalgebra of coinvariants A co ( X ) ↪ A is a Frobenius algebra extension in C . Then we give necessary and sufficient conditions for A co ( X ) ↪ A to be separable, and prove that a Frobenius Galois...
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| Veröffentlicht in: | Mathematische Zeitschrift 2021-02, Vol.297 (1-2), p.25-57 |
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| container_title | Mathematische Zeitschrift |
| container_volume | 297 |
| creator | Bulacu, D. Torrecillas, B. |
| description | We show that a Galois cowreath (
A
,
X
) in a monoidal category
C
is Frobenius if and only if the subalgebra of coinvariants
A
co
(
X
)
↪
A
is a Frobenius algebra extension in
C
. Then we give necessary and sufficient conditions for
A
co
(
X
)
↪
A
to be separable, and prove that a Frobenius Galois cowreath is separable if and only if it admits a total integral. |
| doi_str_mv | 10.1007/s00209-020-02495-8 |
| format | Article |
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A
,
X
) in a monoidal category
C
is Frobenius if and only if the subalgebra of coinvariants
A
co
(
X
)
↪
A
is a Frobenius algebra extension in
C
. Then we give necessary and sufficient conditions for
A
co
(
X
)
↪
A
to be separable, and prove that a Frobenius Galois cowreath is separable if and only if it admits a total integral.</description><identifier>ISSN: 0025-5874</identifier><identifier>EISSN: 1432-1823</identifier><identifier>DOI: 10.1007/s00209-020-02495-8</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Mathematics ; Mathematics and Statistics</subject><ispartof>Mathematische Zeitschrift, 2021-02, Vol.297 (1-2), p.25-57</ispartof><rights>Springer-Verlag GmbH Germany, part of Springer Nature 2020</rights><rights>Springer-Verlag GmbH Germany, part of Springer Nature 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-121ac09c6390d381e293563599297bdd84cdb5558244da59fb215b19a7328edf3</citedby><cites>FETCH-LOGICAL-c319t-121ac09c6390d381e293563599297bdd84cdb5558244da59fb215b19a7328edf3</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/s00209-020-02495-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00209-020-02495-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Bulacu, D.</creatorcontrib><creatorcontrib>Torrecillas, B.</creatorcontrib><title>On Frobenius and separable Galois cowreaths</title><title>Mathematische Zeitschrift</title><addtitle>Math. Z</addtitle><description>We show that a Galois cowreath (
A
,
X
) in a monoidal category
C
is Frobenius if and only if the subalgebra of coinvariants
A
co
(
X
)
↪
A
is a Frobenius algebra extension in
C
. Then we give necessary and sufficient conditions for
A
co
(
X
)
↪
A
to be separable, and prove that a Frobenius Galois cowreath is separable if and only if it admits a total integral.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0025-5874</issn><issn>1432-1823</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9UMtKxDAUDaJgHf0BVwWXEs1zkruUwRmFgdnoOuRV7VDbMWkR_95oBXdeuOcuzuPCQeiSkhtKiLrNhDACuEBZARLrI1RRwRmmmvFjVBVeYqmVOEVnOe8JKaQSFbre9fU6DS727ZRr24c6x4NN1nWx3thuaHPth48U7fiaz9FJY7scL37vAj2v759WD3i72zyu7rbYcwojpoxaT8AvOZDANY0MuFxyCcBAuRC08MFJKTUTIlgJjWNUOgpWcaZjaPgCXc25hzS8TzGPZj9MqS8vDRMKyiguiorNKp-GnFNszCG1bzZ9GkrMdylmLsUUMD-lGF1MfDblIu5fYvqL_sf1BaYaYjQ</recordid><startdate>20210201</startdate><enddate>20210201</enddate><creator>Bulacu, D.</creator><creator>Torrecillas, B.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20210201</creationdate><title>On Frobenius and separable Galois cowreaths</title><author>Bulacu, D. ; Torrecillas, B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-121ac09c6390d381e293563599297bdd84cdb5558244da59fb215b19a7328edf3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bulacu, D.</creatorcontrib><creatorcontrib>Torrecillas, B.</creatorcontrib><collection>CrossRef</collection><jtitle>Mathematische Zeitschrift</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bulacu, D.</au><au>Torrecillas, B.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Frobenius and separable Galois cowreaths</atitle><jtitle>Mathematische Zeitschrift</jtitle><stitle>Math. Z</stitle><date>2021-02-01</date><risdate>2021</risdate><volume>297</volume><issue>1-2</issue><spage>25</spage><epage>57</epage><pages>25-57</pages><issn>0025-5874</issn><eissn>1432-1823</eissn><abstract>We show that a Galois cowreath (
A
,
X
) in a monoidal category
C
is Frobenius if and only if the subalgebra of coinvariants
A
co
(
X
)
↪
A
is a Frobenius algebra extension in
C
. Then we give necessary and sufficient conditions for
A
co
(
X
)
↪
A
to be separable, and prove that a Frobenius Galois cowreath is separable if and only if it admits a total integral.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00209-020-02495-8</doi><tpages>33</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0025-5874 |
| ispartof | Mathematische Zeitschrift, 2021-02, Vol.297 (1-2), p.25-57 |
| issn | 0025-5874 1432-1823 |
| language | eng |
| recordid | cdi_proquest_journals_2479999734 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Mathematics Mathematics and Statistics |
| title | On Frobenius and separable Galois cowreaths |
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