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Answers
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Algebra with positive definite symmetrizing trace is semisimple.
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For what reductive groups $G$ over $K$ are the inner forms classified by $H^1(K, G^{ad})$?
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Has the Lie group E8 really been detected experimentally?
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Occurrence of semi-spin groups
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Which groups have only real and quaternionic irreducible representations?
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How do Jordan algebras help one understand representations of exceptional Lie algebras?
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What is the Implicit Function Theorem good for?
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Uniqueness of maximal subfields
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Simplicity of (complex) orthogonal groups
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Division algebras in which every proper subfield is maximal
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substitute for Serre’s twisting when the “twisting” is outer
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Wanted: Quadratic Space in Characteristic 2 as a Counterexample to a Theorem of Arf