# Characterization of Certain T-ideals from the view point of representation theory of the Symmetric Groups

Volichenko, I. B.; Zalesskii, A. E.

Serdica Mathematical Journal (2012)

- Volume: 38, Issue: 1-3, page 211-236
- ISSN: 1310-6600

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topVolichenko, I. B., and Zalesskii, A. E.. "Characterization of Certain T-ideals from the view point of representation theory of the Symmetric Groups." Serdica Mathematical Journal 38.1-3 (2012): 211-236. <http://eudml.org/doc/288260>.

@article{Volichenko2012,

abstract = {2010 Mathematics Subject Classification: 08B20, 16R10, 16R40, 20C30.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.},

author = {Volichenko, I. B., Zalesskii, A. E.},

journal = {Serdica Mathematical Journal},

keywords = {T-Ideals; Free Associative Algebras},

language = {eng},

number = {1-3},

pages = {211-236},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Characterization of Certain T-ideals from the view point of representation theory of the Symmetric Groups},

url = {http://eudml.org/doc/288260},

volume = {38},

year = {2012},

}

TY - JOUR

AU - Volichenko, I. B.

AU - Zalesskii, A. E.

TI - Characterization of Certain T-ideals from the view point of representation theory of the Symmetric Groups

JO - Serdica Mathematical Journal

PY - 2012

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 38

IS - 1-3

SP - 211

EP - 236

AB - 2010 Mathematics Subject Classification: 08B20, 16R10, 16R40, 20C30.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.

LA - eng

KW - T-Ideals; Free Associative Algebras

UR - http://eudml.org/doc/288260

ER -

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