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Matematicheskie Zametki, 2012, Volume 92, Issue 3, Pages 417–425
DOI: https://doi.org/10.4213/mzm8970
(Mi mzm8970)
 

On Ideals of the Group Algebra of an Infinite Symmetric Group over a Field of Characteristic $p$

A. R. Kemer

Ulyanovsk State University
References:
Abstract: We prove that any nonzero ideal of the group algebra of the infinite symmetric group over a field of nonzero characteristic contains skew-symmetric and symmetric elements of sufficiently large order. Using this result, we reduce the question of the classification of the ideals of the group algebra of the infinite symmetric group to the classification of certain subspaces of the tensor square of a finitely generated free associative algebra.
Keywords: group algebra, ideal of a group algebra, multilinear polynomial, infinite symmetric group, finitely generated free associative algebra, tensor square.
Received: 12.10.2010
English version:
Mathematical Notes, 2012, Volume 92, Issue 3, Pages 375–382
DOI: https://doi.org/10.1134/S0001434612090106
Bibliographic databases:
Document Type: Article
UDC: 512.552
Language: Russian
Citation: A. R. Kemer, “On Ideals of the Group Algebra of an Infinite Symmetric Group over a Field of Characteristic $p$”, Mat. Zametki, 92:3 (2012), 417–425; Math. Notes, 92:3 (2012), 375–382
Citation in format AMSBIB
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