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arXiv · 2103.04575

Elementary equivalence of Kac-Moody groups

Jun Morita·Eugene Plotkin
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Abstract

The paper is devoted to model-theoretic properties of Kac-Moody groups with the focus on elementary equivalence of Kac-Moody groups. We show that elementary equivalence of (untwisted) affine Kac-Moody groups implies coincidence of their generalized Cartan matrices and the elementary equivalence of their ground fields. We also show that elementary equivalence of arbitrary Kac-Moody groups over finite fields implies coincidence of these fields and an isomorphism of their twin root data. The similar result is established for Kac-Moody groups defined over infinite subfields of the algebraic closures of finite fields.

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Jun Morita, Eugene Plotkin. 2021-03-08. Elementary equivalence of Kac-Moody groups. https://arxiv.org/abs/2103.04575

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