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Results tagged with quadratic-forms
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user 6486
Algebraic and geometric theory of quadratic forms and symmetric bilinear forms, e.g., values attained by quadratic forms, isotropic subspaces, the Witt ring, invariants of quadratic forms, the discriminant and Clifford algebra of a quadratic form, Pfister forms, automorphisms of quadratic forms.
17
votes
Accepted
Wanted: Quadratic Space in Characteristic 2 as a Counterexample to a Theorem of Arf
I forwarded this question to Detlev Hoffmann, who says that such examples exist. Specifically, you can produce such an example where there is, say, an anisotropic form of dimension 8 using characteri …
- 2,178
9
votes
Accepted
Is a 8-dimensional quadratic form recognized by its Lie algebra, modulo equivalence and scal...
Yes: Proposition C.3.14 in Brian Conrad's article Reductive group schemes is that $SO(q)$ determines $q$ up to similarity for all $q$ of dimension $> 2$. (This was pointed out by @user74230 in a comm …
- 2,178
3
votes
Accepted
Constructing groups of Type E^{66}_{7,1} having non trivial Tits algebra
This question was posed by Jacques Tits on page 215 of his 1971 paper "Représentations linéaires irréductibles d'un groupe réductif sur un corps quelconque". (He emphasizes: "It would be interesting …
- 2,178
2
votes
Accepted
An isomorphic classification of non-associative division octonion algebras
Yes, the number of isomorphism classes can be greater than 1 and it can be infinite.
One good reference on octonions is the book [1] by Springer-Veldkamp. It gives the following example on page 22:
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- 2,178