Rank varieties and projectivity for a class of local algebras
We consider algebras K[X1,... , Xm]/(X i2), where K is an algebraically closed fields. To any finite dimensional module for this algebra we associate a rank variety. When char(K) = 2 we recover Carlson's rank variety. The main result states that a module is projective if and only if its rank va...
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| Format: | Journal article |
| Language: | English |
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2004
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| _version_ | 1826261071414951936 |
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| author | Erdmann, K Holloway, M |
| author_facet | Erdmann, K Holloway, M |
| author_sort | Erdmann, K |
| collection | OXFORD |
| description | We consider algebras K[X1,... , Xm]/(X i2), where K is an algebraically closed fields. To any finite dimensional module for this algebra we associate a rank variety. When char(K) = 2 we recover Carlson's rank variety. The main result states that a module is projective if and only if its rank variety vanishes. This has applications to other algebras, including tensor products of certain Brauer tree algebras and certain parabolic Hecke algebras. In addition, the result has implications for the graph structure of the stable Auslander-Reiten quiver. |
| first_indexed | 2024-03-06T19:15:48Z |
| format | Journal article |
| id | oxford-uuid:18508f71-4e71-4401-81bd-9ee0c9fdf427 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:15:48Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:18508f71-4e71-4401-81bd-9ee0c9fdf4272022-03-26T10:42:38ZRank varieties and projectivity for a class of local algebrasJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:18508f71-4e71-4401-81bd-9ee0c9fdf427EnglishSymplectic Elements at Oxford2004Erdmann, KHolloway, MWe consider algebras K[X1,... , Xm]/(X i2), where K is an algebraically closed fields. To any finite dimensional module for this algebra we associate a rank variety. When char(K) = 2 we recover Carlson's rank variety. The main result states that a module is projective if and only if its rank variety vanishes. This has applications to other algebras, including tensor products of certain Brauer tree algebras and certain parabolic Hecke algebras. In addition, the result has implications for the graph structure of the stable Auslander-Reiten quiver. |
| spellingShingle | Erdmann, K Holloway, M Rank varieties and projectivity for a class of local algebras |
| title | Rank varieties and projectivity for a class of local algebras |
| title_full | Rank varieties and projectivity for a class of local algebras |
| title_fullStr | Rank varieties and projectivity for a class of local algebras |
| title_full_unstemmed | Rank varieties and projectivity for a class of local algebras |
| title_short | Rank varieties and projectivity for a class of local algebras |
| title_sort | rank varieties and projectivity for a class of local algebras |
| work_keys_str_mv | AT erdmannk rankvarietiesandprojectivityforaclassoflocalalgebras AT hollowaym rankvarietiesandprojectivityforaclassoflocalalgebras |