Extended G-vertex colored partition algebras as centralizer algebras of symmetric groups
The Partition algebras Pk(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 Pbk(x,G), which contain partition algebras Pk(x), as subalgebras. We generalized Jones result by showing...
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| Date: | 2005 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2005
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/156627 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Extended G-vertex colored partition algebras as centralizer algebras of symmetric groups / M. Parvathi, A.J. Kennedy // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 2. — С. 58–79. — Бібліогр.: 13 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1566272025-02-09T11:51:33Z Extended G-vertex colored partition algebras as centralizer algebras of symmetric groups Parvathi, M. Kennedy, A.J. The Partition algebras Pk(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 Pbk(x,G), which contain partition algebras Pk(x), as subalgebras. We generalized Jones result by showing that for a finite group G, the algebra Pbk(n,G) is the centralizer algebra of an action of the symmetric group Sn on tensor space W⊗k , where W = C n|G| . Further we show that these algebras Pbk(x,G) contain as subalgebras the “G-Vertex Colored Partition Algebras Pk(x,G)," introduced in [PK1]. 2005 Article Extended G-vertex colored partition algebras as centralizer algebras of symmetric groups / M. Parvathi, A.J. Kennedy // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 2. — С. 58–79. — Бібліогр.: 13 назв. — англ. 1726-3255 1991 Mathematics Subject Classification: 16S99. https://nasplib.isofts.kiev.ua/handle/123456789/156627 en Algebra and Discrete Mathematics application/pdf Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The Partition algebras Pk(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 Pbk(x,G), which contain partition algebras Pk(x), as
subalgebras. We generalized Jones result by showing that for a
finite group G, the algebra Pbk(n,G) is the centralizer algebra of
an action of the symmetric group Sn on tensor space W⊗k
, where
W = C
n|G|
. Further we show that these algebras Pbk(x,G) contain
as subalgebras the “G-Vertex Colored Partition Algebras Pk(x,G),"
introduced in [PK1]. |
| format |
Article |
| author |
Parvathi, M. Kennedy, A.J. |
| spellingShingle |
Parvathi, M. Kennedy, A.J. Extended G-vertex colored partition algebras as centralizer algebras of symmetric groups Algebra and Discrete Mathematics |
| author_facet |
Parvathi, M. Kennedy, A.J. |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2005 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/156627 |
| citation_txt |
Extended G-vertex colored partition algebras as centralizer algebras of symmetric groups / M. Parvathi, A.J. Kennedy // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 2. — С. 58–79. — Бібліогр.: 13 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT parvathim extendedgvertexcoloredpartitionalgebrasascentralizeralgebrasofsymmetricgroups AT kennedyaj extendedgvertexcoloredpartitionalgebrasascentralizeralgebrasofsymmetricgroups |
| first_indexed |
2025-11-25T22:33:40Z |
| last_indexed |
2025-11-25T22:33:40Z |
| _version_ |
1849803429311938560 |