Notes on some examples for GL₂(Z[t,1/t])

by Markus Rost (Notes, February 2014, 14 pages)

Matt Zaremsky has shown that

(13+11t, 121)

is elementary over Z[t,1/t], i. e., it is a column of a product of upper and lower triangular matrices in GL₂(Z[t,1/t]).

We extend his method and show that for integers m, n (n odd) the vectors

(n+1+nt, n^2), (m+2+mt, m^2), (n+1+nt, 2n^2)

are elementary over Z[t,1/t].

Full text (February 20, 2014): [pdf]

Notes on some examples for GL2(Z[t,1/t])