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

A. R. Kemer

Ulyanovsk State University

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.

UDC: 512.552

Received: 12.10.2010

DOI: 10.4213/mzm8970

 English version: Mathematical Notes, 2012, 92:3, 375–382

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