Abstract simplicity of locally compact Kac-Moody groups

Marquis, Timothée
(2014) Compositio Mathematica — Vol. 150, n° 4, p. 713-728 (2014)

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Abstract
In this paper, we establish that complete Kac-Moody groups over finite fields are abstractly simple. The proof makes essential use of Mathieu and Rousseau's construction of complete Kac-Moody groups over fields. This construction has the advantage that both real and imaginary root spaces of the Lie algebra lift to root subgroups over arbitrary fields. A key point in our proof is the fact, of independent interest, that both real and imaginary root subgroups are contracted by conjugation of positive powers of suitable Weyl group elements. © The Author 2014.
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Marquis, T. (2014). Abstract simplicity of locally compact Kac-Moody groups. Compositio Mathematica, 150(4), 713-728. https://doi.org/10.1112/S0010437X13007598 (Original work published 2014)