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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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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]. |
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