Forms over fields and Witt's lemma

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We give an overview of the general framework of forms of Bak, Tits and Wall, when restricting to vector spaces over fields, and describe its relationship to the classical notions of Hermitian, alternating and quadratic forms. We then prove a version of Witt's lemma in this context, showing in particular that the action of the group of isometries of a space equipped with a form is transitive on isometric subspaces.
Original languageEnglish
JournalMathematica Scandinavica
Issue number3
Pages (from-to)401-423
Publication statusPublished - 2020

Bibliographical note

Final version, to appear in Math. Scand

    Research areas

  • math.KT, math.AT

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