University of Birmingham > Talks@bham > Algebra Seminar > Curtis–Tits Groups of simply-laced type

Curtis–Tits Groups of simply-laced type

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The classification of Curtis-Tits amalgams with triangle-free, simply-laced diagram over a field of size at least 4 divides them into two major classes: Orientable amalgams are those arising from applying the Curtis-Tits theorem to groups of Kac-Moody type, and indeed, their universal completions are central extensions of those groups of Kac-Moody type. In the case of a Ãn−1, all completions can be described as central extensions of concrete (matrix) groups. For non-orientable amalgams these groups are symmetry groups of certain unitary forms over a ring of skew Laurent polynomials. It was conjectured that in fact all amalgams arising from the classification have nontrivial completions. In this talk I will discuss this conjecture and describe some properties of the resulting groups.

This talk is part of the Algebra Seminar series.

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