Abstract
Let S3 denote the Grassmann T-space generated by the commutator [x1,x2,x3] in the free associative algebra K〈x1,x2,…〉 over a field K of characteristic zero. We construct an explicit linear basis for each KSn-module S3∩Pn, where Pn is the space of all multilinear polynomials of degree n in indeterminates x1,…,xn. This provides a solution to the problem of finding a linear basis for S3, which was posed by Latyshev in circa 1990.
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