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Search: MSC category 03C60 ( Model-theoretic algebra [See also 08C10, 12Lxx, 13L05] )

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1. CJM 2008 (vol 60 pp. 88)

 Nilpotent Conjugacy Classes in $p$-adic Lie Algebras: The Odd Orthogonal Case We will study the following question: Are nilpotent conjugacy classes of reductive Lie algebras over $p$-adic fields definable? By definable, we mean definable by a formula in Pas's language. In this language, there are no field extensions and no uniformisers. Using Waldspurger's parametrization, we answer in the affirmative in the case of special orthogonal Lie algebras $\mathfrak{so}(n)$ for $n$ odd, over $p$-adic fields. Categories:17B10, 03C60