Extended \(G\)-vertex colored partition algebras as centralizer algebras of symmetric groups
The Partition algebras \(P_k(x)\) have been defined in [M1] and [Jo]. We introduce a new class of algebras for every group \(G\) called ``Extended \(G\)-Vertex Colored Partition Algebras," denoted by \(\widehat{P}_{k}(x,G)\), which contain partition algebras \(P_k(x)\), as subalgebras. We gener...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/936 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| id |
admjournalluguniveduua-article-936 |
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admjournalluguniveduua-article-9362018-03-21T06:34:59Z Extended \(G\)-vertex colored partition algebras as centralizer algebras of symmetric groups Parvathi, M. Kennedy, A. Joseph Partition algebra, centralizer algebra, direct product, wreath product, symmetric group 16S99 The Partition algebras \(P_k(x)\) have been defined in [M1] and [Jo]. We introduce a new class of algebras for every group \(G\) called ``Extended \(G\)-Vertex Colored Partition Algebras," denoted by \(\widehat{P}_{k}(x,G)\), which contain partition algebras \(P_k(x)\), as subalgebras. We generalized Jones result by showing that for a finite group \(G\), the algebra \(\widehat{P}_{k}(n,G)\) is the centralizer algebra of an action of the symmetric group \(S_n \) on tensor space \(W^{\otimes k}\), where \(W=\mathbb{C}^{n|G|}\). Further we show that these algebras \(\widehat{P}_{k}(x,G)\) contain as subalgebras the ``\(G\)-Vertex Colored Partition Algebras \({P_{k}(x,G)}\)," introduced in [PK1]. 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/936 Algebra and Discrete Mathematics; Vol 4, No 2 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/936/465 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2018-03-21T06:34:59Z |
| collection |
OJS |
| language |
English |
| topic |
Partition algebra centralizer algebra direct product wreath product symmetric group 16S99 |
| spellingShingle |
Partition algebra centralizer algebra direct product wreath product symmetric group 16S99 Parvathi, M. Kennedy, A. Joseph Extended \(G\)-vertex colored partition algebras as centralizer algebras of symmetric groups |
| topic_facet |
Partition algebra centralizer algebra direct product wreath product symmetric group 16S99 |
| format |
Article |
| author |
Parvathi, M. Kennedy, A. Joseph |
| author_facet |
Parvathi, M. Kennedy, A. Joseph |
| author_sort |
Parvathi, M. |
| title |
Extended \(G\)-vertex colored partition algebras as centralizer algebras of symmetric groups |
| title_short |
Extended \(G\)-vertex colored partition algebras as centralizer algebras of symmetric groups |
| title_full |
Extended \(G\)-vertex colored partition algebras as centralizer algebras of symmetric groups |
| title_fullStr |
Extended \(G\)-vertex colored partition algebras as centralizer algebras of symmetric groups |
| title_full_unstemmed |
Extended \(G\)-vertex colored partition algebras as centralizer algebras of symmetric groups |
| title_sort |
extended \(g\)-vertex colored partition algebras as centralizer algebras of symmetric groups |
| description |
The Partition algebras \(P_k(x)\) have been defined in [M1] and [Jo]. We introduce a new class of algebras for every group \(G\) called ``Extended \(G\)-Vertex Colored Partition Algebras," denoted by \(\widehat{P}_{k}(x,G)\), which contain partition algebras \(P_k(x)\), as subalgebras. We generalized Jones result by showing that for a finite group \(G\), the algebra \(\widehat{P}_{k}(n,G)\) is the centralizer algebra of an action of the symmetric group \(S_n \) on tensor space \(W^{\otimes k}\), where \(W=\mathbb{C}^{n|G|}\). Further we show that these algebras \(\widehat{P}_{k}(x,G)\) contain as subalgebras the ``\(G\)-Vertex Colored Partition Algebras \({P_{k}(x,G)}\)," introduced in [PK1]. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/936 |
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AT parvathim extendedgvertexcoloredpartitionalgebrasascentralizeralgebrasofsymmetricgroups AT kennedyajoseph extendedgvertexcoloredpartitionalgebrasascentralizeralgebrasofsymmetricgroups |
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2025-12-02T15:37:41Z |
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2025-12-02T15:37:41Z |
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1850411435763433472 |