Free subgroups in k(x(1), ... , x(n))(X; sigma) and k(x, y)(X; sigma)

Author(s)

Goncalves, Jairo Z.

• Document type: Journal article
• Source: FORUM MATHEMATICUM; v. 31, n. 3, p. 769-777, MAY 2019.
• Web of Science Citations: 0

Abstract

Let k be a field, let A1 be the k-algebra k{[}x(1)(+/- 1),..., x(s)(+/- 1)] of Laurent polynomials in x(1),..., x(s), and let A2 be the k-algebra k{[}x, y] of polynomials in the commutative indeterminates x and y. Let sigma(1) be the monomial k-automorphism of A1 given by A = (a(i,j)) is an element of GL(s)(Z) and sigma(1)(x(i)) =Pi(s)(j=1) x(j)(ai,j), 1 <= i <= s, and let sigma(2) is an element of Aut(k)(k{[}x, y]). Let D-i, 1 <= i <= 2, be the ring of fractions of the skew polynomial ring A(i){[}X; sigma(i)], and let D-i(center dot) be its multiplicative group. Under a mild restriction for D-1, and in general for D-2, we show that D-i(center dot), 1 <= i <= 2, contains a free subgroup. If i = 1 and s = 2, we show that a noncentral normal subgroup N of D-1(center dot) contains a free subgroup. (AU)

• FAPESP's process: 15/09162-9 - Non commutative algebra and applications
• Grantee: Francisco Cesar Polcino Milies
• Support Opportunities: Research Projects - Thematic Grants