The elementary polynomials in noncommuting variables
Samuel S. Holland
Abstract
We study the ring generated over a field of characteristic 0 by noncommuting indeterminates x1,x2,...,xn subject only to the relations xiσk=σk xi, for i,k=1,2,...,n, and their consequences, where σk =σk(x1,x2,...,xn) is the k-th elementary polynomial in the noncommuting variables xi. We assume n≥ 3 throughout.
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