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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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2005
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/156608 |
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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. |
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