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        • Associative Rings
          • Ariki-Koike Algebras
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          • KLR Algebras
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        • Commutative Algebra
        • Fusion Systems
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          • Associative Rings
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          • Fusion Systems
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            • Algebraic Groups
            • Combinatorial Group Theory
            • Computational Group Theory
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            • Geometric Group Theory
            • Infinite Groups
            • Lie Groups
            • Permutation Groups
          • Lie Theory
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            • Lie Algebras
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            • Lie Algebras
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            • Representations of Lie Algebras
            • Representations of Symmetric Groups
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      Lie groups (Borcherds)

      Richard Borcherds: Lie Groups, VII. Positive characteristic is weird

      20th February, 2021
      Watch LaterRemove Cinema Mode

      The previous lecture in this series is here. The next lecture in this series is here.

      We give several examples to show that, over fields of positive characteristic, Lie algebras can behave strangely, and have a weaker connection to Lie groups. In particular the Lie algebra does not generate the ring of all invariant differential operators.

      This video is part of a lecture course by Richard Borcherds from 2021.

      In This Lecture Course

      • Richard Borcherds: Lie Groups, I. Introduction
      • Richard Borcherds: Lie Groups, II. Lie algebras
      • Richard Borcherds: Lie Groups, III. Lie groups and Lie algebras
      • Richard Borcherds: Lie Groups, IV. Exponential map
      • Richard Borcherds: Lie Groups, V. Baker-Campbell-Hausdorff formula
      • Richard Borcherds: Lie Groups, VI. Poincaré-Birkhoff-Witt theorem
      • Richard Borcherds: Lie Groups, VII. Positive characteristic is weird
      • Richard Borcherds: Lie Groups, VIII. Bianchi classification
      • Richard Borcherds: Lie Groups, IX. Engel’s theorem
      • Richard Borcherds: Lie Groups, X. Lie’s theorem
      • Richard Borcherds: Lie Groups, XI. Haar measure

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