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 ⇔ it is of finite type ⇔ the poset with n...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2005 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2005
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/156608 |
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| Zitieren: | On representation type of a pair of posets with involution / V.M. Bondarenko // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 1–7. — Бібліогр.: 12 назв. — англ. |
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Bondarenko, V.M. 2019-06-18T17:49:52Z 2019-06-18T17:49:52Z 2005 On representation type of a pair of posets with involution / V.M. Bondarenko // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 1–7. — Бібліогр.: 12 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 15A, 16G. https://nasplib.isofts.kiev.ua/handle/123456789/156608 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 ⇔ it is of finite type ⇔ 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. Dedicated to Yu.A. Drozd on the occasion of his 60th birthday en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On representation type of a pair of posets with involution Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On representation type of a pair of posets with involution |
| spellingShingle |
On representation type of a pair of posets with involution Bondarenko, V.M. |
| 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 |
| author |
Bondarenko, V.M. |
| author_facet |
Bondarenko, V.M. |
| publishDate |
2005 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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 ⇔ it is of finite type ⇔ 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/156608 |
| citation_txt |
On representation type of a pair of posets with involution / V.M. Bondarenko // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 1–7. — Бібліогр.: 12 назв. — англ. |
| work_keys_str_mv |
AT bondarenkovm onrepresentationtypeofapairofposetswithinvolution |
| first_indexed |
2025-12-07T16:15:52Z |
| last_indexed |
2025-12-07T16:15:52Z |
| _version_ |
1850866822845300736 |