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Title: Characterization of Certain T-ideals from the view point of representation theory of the Symmetric Groups
Authors: Volichenko, I. B.
Zalesskii, A. E.
Keywords: T-Ideals
Free Associative Algebras
Issue Date: 2012
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 38, No 1-3, (2012), 211p-236p
Abstract: Let K[X] be a free associative algebra (without identity) over a field K of characteristic 0 with free generators X = (X1, X2, ...), and let Pn be the set of all multilinear elements of degree n in K[X]. Then Pn is a KSn-module, where KSn is the group algebra of the symmetric group Sn. An ideal of K[X] stable under all endomorphisms of K[X] is called a T-ideal. If L is an arbitrary T-ideal of K[X] then Ln := Pn ∩ L is a KSn-module too. An important task in the theory of varieties of algebras is to reveal general regularities in the behavior of the sequence A n for various T-ideals A. In certain cases, given a property P, say, of the sequence, one can find a T-ideal L(P) such that a T-ideal L′ satisfies P if and only if L′ contains L(P). The results of this paper have to be regarded from this point of view.
Description: 2010 Mathematics Subject Classification: 08B20, 16R10, 16R40, 20C30.
ISSN: 1310-6600
Appears in Collections:Volume 38, Number 1-3

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