Projective embeddings of dual polar spaces of mixed type
نویسندگان
چکیده
منابع مشابه
Projective embeddings of dual polar spaces arising from a class of alternative division rings
We discuss some recent results of us regarding a class of polar spaces which includes the nonembeddable polar spaces introduced by Tits [3]. These results include an elementary construction of the polar space, a construction of a polarized embedding of the corresponding dual polar space and the determination whether this projective embedding is universal and unique (as a polarized embedding).
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Let n ≥ 2, let K,K′ be fields such that K′ is a quadratic Galoisextension of K and let θ denote the unique nontrivial element in Gal(K′/K). Suppose the symplectic dual polar space DW (2n− 1,K) is fully and isometrically embedded into the Hermitian dual polar space DH(2n − 1,K′, θ). We prove that the projective embedding of DW (2n − 1,K) induced by the Grassmann-embedding of DH(2n − 1,K′, θ) is ...
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In this article, two different notions of embeddings of polar spaces are compared. By using existing results in the field, a statement for a Fundamental Theorem of Polar Geometry is then obtained.
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Let be a thick dual polar space of rank n ≥ 2 admitting a full polarized embedding e in a finite-dimensional projective space , i.e., for every point x of , e maps the set of points of at non-maximal distance from x into a hyperplane e∗(x) of . Using a result of Kasikova and Shult [11], we are able the show that there exists up to isomorphisms a unique full polarized embedding of of minimal dim...
متن کاملPolarized and homogeneous embeddings of dual polar spaces
Let Γ be the dual of a classical polar space and let e be a projective embedding of Γ, defined over a commutative division ring. We shall prove that, if e is homogeneous, then it is polarized. MSC 2000: 51B25, 51E24, 51A45, 51A50.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2016
ISSN: 0024-3795
DOI: 10.1016/j.laa.2016.03.032