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

Volichenko, 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 -