Isomorphisms of groups of Kac–Moody type over 𝔽 ₂

Abstract Caprace and Mühlherr (2006) solved the isomorphism problem for Kac–Moody groups of non-spherical type over finite fields of cardinality at least 4. In this paper, we solve the isomorphism problem for groups of Kac–Moody type (e.g. Kac–Moody groups) over <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi mathvariant="double-struck">F</m:mi> <m:mn>2</m:mn> </m:msub> </m:math> \mathbb{F}_{2} whose type is 2-complete and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mover accent="true"> <m:mi>A</m:mi> <m:mo>̃</m:mo> </m:mover> <m:mn>2</m:mn> </m:msub> </m:math> \tilde{A}_{2} -free.