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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Published in:Algebra and Discrete Mathematics
Date:2005
Main Author: Bondarenko, V.M.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2005
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/156608
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this: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
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Summary: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