On the factorability of polynomial identities of upper block triangular matrix algebras graded by cyclic groups
Let F be an algebraically closed field of characteristic zero and G be an arbitrary finite cyclic group. In this paper, given an m-tuple (A1,…,Am) of finite dimensional G-simple algebras, we focus on the study of the factorability of the TG-ideals IdG((UT(A1,…,Am),α˜)) of the G-graded upper block tr...
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| Veröffentlicht in: | Linear algebra and its applications 2020-09, Vol.601, p.311-337 |
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| creator | Di Vincenzo, Onofrio Mario Pinto, Marcos Antônio da Silva da Silva, Viviane Ribeiro Tomaz |
| description | Let F be an algebraically closed field of characteristic zero and G be an arbitrary finite cyclic group. In this paper, given an m-tuple (A1,…,Am) of finite dimensional G-simple algebras, we focus on the study of the factorability of the TG-ideals IdG((UT(A1,…,Am),α˜)) of the G-graded upper block triangular matrix algebras UT(A1,…,Am) endowed with elementary G-gradings induced by some maps α˜.
When G is a cyclic p-group we prove that the factorability of the ideal IdG((UT(A1,…,Am),α˜) is equivalent to the G-regularity of all (except for at most one) the G-simple components A1,…,Am, as well to the existence of a unique isomorphism class of α˜-admissible elementary G-gradings for UT(A1,…,Am). Moreover, we present some necessary and sufficient conditions to the factorability of IdG((UT(A1,A2),α˜)), even in case G is not a p-group, with some stronger assumptions on the gradings of the algebras A1 and A2. |
| doi_str_mv | 10.1016/j.laa.2020.05.008 |
| format | Article |
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When G is a cyclic p-group we prove that the factorability of the ideal IdG((UT(A1,…,Am),α˜) is equivalent to the G-regularity of all (except for at most one) the G-simple components A1,…,Am, as well to the existence of a unique isomorphism class of α˜-admissible elementary G-gradings for UT(A1,…,Am). Moreover, we present some necessary and sufficient conditions to the factorability of IdG((UT(A1,A2),α˜)), even in case G is not a p-group, with some stronger assumptions on the gradings of the algebras A1 and A2.</description><identifier>ISSN: 0024-3795</identifier><identifier>EISSN: 1873-1856</identifier><identifier>DOI: 10.1016/j.laa.2020.05.008</identifier><language>eng</language><publisher>Amsterdam: Elsevier Inc</publisher><subject>Algebra ; Factorability ; G-regularity ; Graded algebras ; Graded polynomial identities ; Invariance subgroups ; Isomorphism ; Linear algebra ; Polynomials</subject><ispartof>Linear algebra and its applications, 2020-09, Vol.601, p.311-337</ispartof><rights>2020 Elsevier Inc.</rights><rights>Copyright American Elsevier Company, Inc. Sep 15, 2020</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c325t-e10737cc707171729888a1b49edbc5ac7bb34fd01bc0e68f2bd6499095e98dcb3</citedby><cites>FETCH-LOGICAL-c325t-e10737cc707171729888a1b49edbc5ac7bb34fd01bc0e68f2bd6499095e98dcb3</cites><orcidid>0000-0003-2543-2515</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.laa.2020.05.008$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Di Vincenzo, Onofrio Mario</creatorcontrib><creatorcontrib>Pinto, Marcos Antônio da Silva</creatorcontrib><creatorcontrib>da Silva, Viviane Ribeiro Tomaz</creatorcontrib><title>On the factorability of polynomial identities of upper block triangular matrix algebras graded by cyclic groups</title><title>Linear algebra and its applications</title><description>Let F be an algebraically closed field of characteristic zero and G be an arbitrary finite cyclic group. In this paper, given an m-tuple (A1,…,Am) of finite dimensional G-simple algebras, we focus on the study of the factorability of the TG-ideals IdG((UT(A1,…,Am),α˜)) of the G-graded upper block triangular matrix algebras UT(A1,…,Am) endowed with elementary G-gradings induced by some maps α˜.
When G is a cyclic p-group we prove that the factorability of the ideal IdG((UT(A1,…,Am),α˜) is equivalent to the G-regularity of all (except for at most one) the G-simple components A1,…,Am, as well to the existence of a unique isomorphism class of α˜-admissible elementary G-gradings for UT(A1,…,Am). Moreover, we present some necessary and sufficient conditions to the factorability of IdG((UT(A1,A2),α˜)), even in case G is not a p-group, with some stronger assumptions on the gradings of the algebras A1 and A2.</description><subject>Algebra</subject><subject>Factorability</subject><subject>G-regularity</subject><subject>Graded algebras</subject><subject>Graded polynomial identities</subject><subject>Invariance subgroups</subject><subject>Isomorphism</subject><subject>Linear algebra</subject><subject>Polynomials</subject><issn>0024-3795</issn><issn>1873-1856</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kE1rHDEMhk1JoJs0PyA3Q84zlT3f5FSWNC0s7KU9G39oNp56x1PbEzr_vl6256KDkPS-kngIeWRQMmDt56l0UpYcOJTQlAD9B7JjfVcVrG_aG7ID4HVRdUPzkdzFOAFA3QHfEX-caXpDOkqdfJDKOps26ke6eLfN_mylo9bgnGyyGC-DdVkwUOW8_kVTsHI-rU4Gepa5-EOlO6EKMtJTkAYNVRvVm3ZW54Zfl_iJ3I7SRXz4l-_Jz68vP_bfisPx9fv-y6HQFW9SgQy6qtO6g47l4EPf95KpekCjdCN1p1RVjwaY0oBtP3Jl2noYYGhw6I1W1T15uu5dgv-9Ykxi8muY80nB6xrqgTe8zSp2VengYww4iiXYswybYCAuXMUkMldx4SqgEZlr9jxfPZjff7cYRNQWZ43GBtRJGG__4_4LS8uCBQ</recordid><startdate>20200915</startdate><enddate>20200915</enddate><creator>Di Vincenzo, Onofrio Mario</creator><creator>Pinto, Marcos Antônio da Silva</creator><creator>da Silva, Viviane Ribeiro Tomaz</creator><general>Elsevier Inc</general><general>American Elsevier Company, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0003-2543-2515</orcidid></search><sort><creationdate>20200915</creationdate><title>On the factorability of polynomial identities of upper block triangular matrix algebras graded by cyclic groups</title><author>Di Vincenzo, Onofrio Mario ; Pinto, Marcos Antônio da Silva ; da Silva, Viviane Ribeiro Tomaz</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c325t-e10737cc707171729888a1b49edbc5ac7bb34fd01bc0e68f2bd6499095e98dcb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Algebra</topic><topic>Factorability</topic><topic>G-regularity</topic><topic>Graded algebras</topic><topic>Graded polynomial identities</topic><topic>Invariance subgroups</topic><topic>Isomorphism</topic><topic>Linear algebra</topic><topic>Polynomials</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Di Vincenzo, Onofrio Mario</creatorcontrib><creatorcontrib>Pinto, Marcos Antônio da Silva</creatorcontrib><creatorcontrib>da Silva, Viviane Ribeiro Tomaz</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Linear algebra and its applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Di Vincenzo, Onofrio Mario</au><au>Pinto, Marcos Antônio da Silva</au><au>da Silva, Viviane Ribeiro Tomaz</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the factorability of polynomial identities of upper block triangular matrix algebras graded by cyclic groups</atitle><jtitle>Linear algebra and its applications</jtitle><date>2020-09-15</date><risdate>2020</risdate><volume>601</volume><spage>311</spage><epage>337</epage><pages>311-337</pages><issn>0024-3795</issn><eissn>1873-1856</eissn><abstract>Let F be an algebraically closed field of characteristic zero and G be an arbitrary finite cyclic group. In this paper, given an m-tuple (A1,…,Am) of finite dimensional G-simple algebras, we focus on the study of the factorability of the TG-ideals IdG((UT(A1,…,Am),α˜)) of the G-graded upper block triangular matrix algebras UT(A1,…,Am) endowed with elementary G-gradings induced by some maps α˜.
When G is a cyclic p-group we prove that the factorability of the ideal IdG((UT(A1,…,Am),α˜) is equivalent to the G-regularity of all (except for at most one) the G-simple components A1,…,Am, as well to the existence of a unique isomorphism class of α˜-admissible elementary G-gradings for UT(A1,…,Am). Moreover, we present some necessary and sufficient conditions to the factorability of IdG((UT(A1,A2),α˜)), even in case G is not a p-group, with some stronger assumptions on the gradings of the algebras A1 and A2.</abstract><cop>Amsterdam</cop><pub>Elsevier Inc</pub><doi>10.1016/j.laa.2020.05.008</doi><tpages>27</tpages><orcidid>https://orcid.org/0000-0003-2543-2515</orcidid></addata></record> |
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| subjects | Algebra Factorability G-regularity Graded algebras Graded polynomial identities Invariance subgroups Isomorphism Linear algebra Polynomials |
| title | On the factorability of polynomial identities of upper block triangular matrix algebras graded by cyclic groups |
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