On representation type of a pair of posets with involution
In this paper we consider the problem on classifying the representations of a pair of posets with involution. We prove that if one of these is a chain of length at least 4 with trivial involution and the other is with nontrivial one, then the pair is tame \(\Leftrightarrow\) it is of finite type...
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| Datum: | 2018 |
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| Sprache: | English |
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Lugansk National Taras Shevchenko University
2018
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oai:ojs.admjournal.luguniv.edu.ua:article-9122018-03-21T07:18:38Z On representation type of a pair of posets with involution Bondarenko, Vitalij M. semichain, tame, wild, representation, category 15A, 16G In this paper we consider the problem on classifying the representations of a pair of posets with involution. We prove that if one of these is a chain of length at least 4 with trivial involution and the other is with nontrivial one, then the pair is tame \(\Leftrightarrow\) it is of finite type \(\Leftrightarrow\) the poset with nontrivial involution is a \(*\)-semichain (\(*\) being the involution). The case that each of the posets with involution is not a chain with trivial one was considered by the author earlier. In proving our result we do not use the known technically difficult results on representation type of posets with involution. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/912 Algebra and Discrete Mathematics; Vol 4, No 1 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/912/441 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-03-21T07:18:38Z |
| collection |
OJS |
| language |
English |
| topic |
semichain tame wild representation category 15A 16G |
| spellingShingle |
semichain tame wild representation category 15A 16G Bondarenko, Vitalij M. On representation type of a pair of posets with involution |
| topic_facet |
semichain tame wild representation category 15A 16G |
| format |
Article |
| author |
Bondarenko, Vitalij M. |
| author_facet |
Bondarenko, Vitalij M. |
| author_sort |
Bondarenko, Vitalij M. |
| title |
On representation type of a pair of posets with involution |
| title_short |
On representation type of a pair of posets with involution |
| title_full |
On representation type of a pair of posets with involution |
| title_fullStr |
On representation type of a pair of posets with involution |
| title_full_unstemmed |
On representation type of a pair of posets with involution |
| title_sort |
on representation type of a pair of posets with involution |
| description |
In this paper we consider the problem on classifying the representations of a pair of posets with involution. We prove that if one of these is a chain of length at least 4 with trivial involution and the other is with nontrivial one, then the pair is tame \(\Leftrightarrow\) it is of finite type \(\Leftrightarrow\) the poset with nontrivial involution is a \(*\)-semichain (\(*\) being the involution). The case that each of the posets with involution is not a chain with trivial one was considered by the author earlier. In proving our result we do not use the known technically difficult results on representation type of posets with involution. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/912 |
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AT bondarenkovitalijm onrepresentationtypeofapairofposetswithinvolution |
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2025-07-17T10:35:53Z |
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2025-07-17T10:35:53Z |
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1837890067369033728 |