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An anti-isomorphism between Brauer–Clifford–Long groups BD(S, H) and BD(Sop,H∗)
For a commutative ring R and a commutative cocommutative Hopf algebra H finitely generated projective as an R -module, Tilborghs in (Math J Okayama Univ 32:43–52, 1990), established an anti-isomorphism of groups between the Brauer group BD ( R , H ) of H -dimodule and the Brauer B D ( R , H ∗ ) of...
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| Published in: | Beiträge zur Algebra und Geometrie 2023-06, Vol.64 (2), p.445-458 |
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| container_title | Beiträge zur Algebra und Geometrie |
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| creator | Nango, Christophe Lopez |
| description | For a commutative ring
R
and a commutative cocommutative Hopf algebra
H
finitely generated projective as an
R
-module, Tilborghs in (Math J Okayama Univ 32:43–52, 1990), established an anti-isomorphism of groups between the Brauer group
BD
(
R
,
H
) of
H
-dimodule and the Brauer
B
D
(
R
,
H
∗
)
of
H
∗
-dimodule algebras, where
H
∗
is the linear dual of
H
. In this paper, we generalize this result by constructing an anti-isomorphism of groups between
BD
(
S
,
H
), the Brauer group of dyslectic (
S
,
H
)-dimodule algebras and
B
D
(
S
op
,
H
∗
)
, the Brauer group of dyslectic
(
S
op
,
H
∗
)
-dimodule algebras, where
S
is an
H
-commutative
H
-dimodule algebra and
S
op
is the opposite algebra of
S
. |
| doi_str_mv | 10.1007/s13366-022-00641-3 |
| format | article |
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R
and a commutative cocommutative Hopf algebra
H
finitely generated projective as an
R
-module, Tilborghs in (Math J Okayama Univ 32:43–52, 1990), established an anti-isomorphism of groups between the Brauer group
BD
(
R
,
H
) of
H
-dimodule and the Brauer
B
D
(
R
,
H
∗
)
of
H
∗
-dimodule algebras, where
H
∗
is the linear dual of
H
. In this paper, we generalize this result by constructing an anti-isomorphism of groups between
BD
(
S
,
H
), the Brauer group of dyslectic (
S
,
H
)-dimodule algebras and
B
D
(
S
op
,
H
∗
)
, the Brauer group of dyslectic
(
S
op
,
H
∗
)
-dimodule algebras, where
S
is an
H
-commutative
H
-dimodule algebra and
S
op
is the opposite algebra of
S
.</description><identifier>ISSN: 0138-4821</identifier><identifier>EISSN: 2191-0383</identifier><identifier>DOI: 10.1007/s13366-022-00641-3</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algebra ; Algebraic Geometry ; Commutativity ; Convex and Discrete Geometry ; Geometry ; Group theory ; Isomorphism ; Mathematics ; Mathematics and Statistics ; Original Paper ; Rings (mathematics)</subject><ispartof>Beiträge zur Algebra und Geometrie, 2023-06, Vol.64 (2), p.445-458</ispartof><rights>The Managing Editors 2022</rights><rights>The Managing Editors 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-604c86943c12f33bd4f5ad46d7c18f4b41c40d1e2fac7bf73775de2a53c05f233</citedby><cites>FETCH-LOGICAL-c319t-604c86943c12f33bd4f5ad46d7c18f4b41c40d1e2fac7bf73775de2a53c05f233</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Nango, Christophe Lopez</creatorcontrib><title>An anti-isomorphism between Brauer–Clifford–Long groups BD(S, H) and BD(Sop,H∗)</title><title>Beiträge zur Algebra und Geometrie</title><addtitle>Beitr Algebra Geom</addtitle><description>For a commutative ring
R
and a commutative cocommutative Hopf algebra
H
finitely generated projective as an
R
-module, Tilborghs in (Math J Okayama Univ 32:43–52, 1990), established an anti-isomorphism of groups between the Brauer group
BD
(
R
,
H
) of
H
-dimodule and the Brauer
B
D
(
R
,
H
∗
)
of
H
∗
-dimodule algebras, where
H
∗
is the linear dual of
H
. In this paper, we generalize this result by constructing an anti-isomorphism of groups between
BD
(
S
,
H
), the Brauer group of dyslectic (
S
,
H
)-dimodule algebras and
B
D
(
S
op
,
H
∗
)
, the Brauer group of dyslectic
(
S
op
,
H
∗
)
-dimodule algebras, where
S
is an
H
-commutative
H
-dimodule algebra and
S
op
is the opposite algebra of
S
.</description><subject>Algebra</subject><subject>Algebraic Geometry</subject><subject>Commutativity</subject><subject>Convex and Discrete Geometry</subject><subject>Geometry</subject><subject>Group theory</subject><subject>Isomorphism</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Rings (mathematics)</subject><issn>0138-4821</issn><issn>2191-0383</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kLtOwzAUhi0EEqXwAkyRWKhUg4_txO7YlkuRKjFwWa3EsUuqNg52IsTGyM7AyrPwKH0S0haJjemcI33_f6QPoWMgZ0CIOA_AWJJgQikmJOGA2Q7qUBgAJkyyXdQhwCTmksI-OghhTlpKCNFBj8MySsu6wEVwS-erpyIso8zUL8aU0cinjfGrt4_xorDW-bxdp66cRTPvmipEo4vTu_7316TXVuSby1X9yer9s3eI9my6CObod3bRw9Xl_XiCp7fXN-PhFGsGgxonhGuZDDjTQC1jWc5tnOY8yYUGaXnGQXOSg6E21SKzggkR54amMdMktpSxLjrZ9lbePTcm1GruGl-2LxWVRBAOUoqWoltKexeCN1ZVvlim_lUBUWt_autPtf7Uxp9aV7NtKLRwOTP-r_qf1A-2KnRk</recordid><startdate>20230601</startdate><enddate>20230601</enddate><creator>Nango, Christophe Lopez</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20230601</creationdate><title>An anti-isomorphism between Brauer–Clifford–Long groups BD(S, H) and BD(Sop,H∗)</title><author>Nango, Christophe Lopez</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-604c86943c12f33bd4f5ad46d7c18f4b41c40d1e2fac7bf73775de2a53c05f233</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algebra</topic><topic>Algebraic Geometry</topic><topic>Commutativity</topic><topic>Convex and Discrete Geometry</topic><topic>Geometry</topic><topic>Group theory</topic><topic>Isomorphism</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><topic>Rings (mathematics)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nango, Christophe Lopez</creatorcontrib><collection>CrossRef</collection><jtitle>Beiträge zur Algebra und Geometrie</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nango, Christophe Lopez</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An anti-isomorphism between Brauer–Clifford–Long groups BD(S, H) and BD(Sop,H∗)</atitle><jtitle>Beiträge zur Algebra und Geometrie</jtitle><stitle>Beitr Algebra Geom</stitle><date>2023-06-01</date><risdate>2023</risdate><volume>64</volume><issue>2</issue><spage>445</spage><epage>458</epage><pages>445-458</pages><issn>0138-4821</issn><eissn>2191-0383</eissn><abstract>For a commutative ring
R
and a commutative cocommutative Hopf algebra
H
finitely generated projective as an
R
-module, Tilborghs in (Math J Okayama Univ 32:43–52, 1990), established an anti-isomorphism of groups between the Brauer group
BD
(
R
,
H
) of
H
-dimodule and the Brauer
B
D
(
R
,
H
∗
)
of
H
∗
-dimodule algebras, where
H
∗
is the linear dual of
H
. In this paper, we generalize this result by constructing an anti-isomorphism of groups between
BD
(
S
,
H
), the Brauer group of dyslectic (
S
,
H
)-dimodule algebras and
B
D
(
S
op
,
H
∗
)
, the Brauer group of dyslectic
(
S
op
,
H
∗
)
-dimodule algebras, where
S
is an
H
-commutative
H
-dimodule algebra and
S
op
is the opposite algebra of
S
.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s13366-022-00641-3</doi><tpages>14</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0138-4821 |
| ispartof | Beiträge zur Algebra und Geometrie, 2023-06, Vol.64 (2), p.445-458 |
| issn | 0138-4821 2191-0383 |
| language | eng |
| recordid | cdi_proquest_journals_2807041887 |
| source | Springer Nature |
| subjects | Algebra Algebraic Geometry Commutativity Convex and Discrete Geometry Geometry Group theory Isomorphism Mathematics Mathematics and Statistics Original Paper Rings (mathematics) |
| title | An anti-isomorphism between Brauer–Clifford–Long groups BD(S, H) and BD(Sop,H∗) |
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