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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Bibliographic Details
Date:2005
Main Authors: Parvathi, M., Kennedy, A.J.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2005
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
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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].