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...
Збережено в:
| Дата: | 2005 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2005
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/156627 |
| Теги: |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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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