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...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2005 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
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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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862691441036230656 |
|---|---|
| author | Bondarenko, V.M. |
| author_facet | Bondarenko, V.M. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-12-07T16:15:52Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-156608 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T16:15:52Z |
| publishDate | 2005 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | On representation type of a pair of posets with involution Bondarenko, V.M. |
| title | 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_short | On representation type of a pair of posets with involution |
| title_sort | on representation type of a pair of posets with involution |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/156608 |
| work_keys_str_mv | AT bondarenkovm onrepresentationtypeofapairofposetswithinvolution |