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arXiv · 1801.03575

The Structure of the Three-Dimensional Special Linear Group over a Local Field

David Wright
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Abstract

For K a local field, it is shown that SL3(K) acts on a simply connected two dimensional simplicial complex in which a single face serves as a fundamental domain. From this it follows that SL3(K) is the generalized amalgamated product of three subgroups. Specifically if K is the field of fractions of the discrete valuation ring O, then SL3(K) is the amalgamation of three subgroups isomorphic to SL3(O) along pairwise intersections. This generalizes a theorem of Ihara, which gives the structure of SL2(K) as the amalgamated product of two groups in analogous fashion.

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David Wright. 2018-01-10. The Structure of the Three-Dimensional Special Linear Group over a Local Field. https://arxiv.org/abs/1801.03575

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