87,386 research outputs found
Non-projective embeddings in the grassmann variety
No full texte investigate properties of the grassmann embedding of dual classical thick generalized quadrangles focusing on the grassmann embedding of the dual of an orthogonal quadrangle and the dual of a hermitian quadrangle We prove that, if the characteristic of the field is different from 2 then the dimension of the grassmann embedding of is and its image is isomorphic to the quadratic veronese variety of a 3-dimensional projective space. If is a perfect field of characteristic 2 then the dimension of the grassmann embedding of is proved to be and its image is a -dimensional algebraic subvariety of the grassmannian of lines of a -dimensional projective space.
Moving to consider the dual quadrangle , we prove that the dimension of its grassmann embedding is and the image of under the grassmann embedding is a -dimensional algebraic subvariety of the grassmannian of lines of a -dimensional projective space
Neifeld’s Connection Inducedon the Grassmann Manifold
No full textsummary:The work concerns to investigations in the field of differential geometry. It is realized by a method of continuations and scopes of G. F. Laptev which generalizes a moving frame method and Cartan’s exterior forms method and depends on calculation of exterior differential forms. The Grassmann manifold (space of all -planes) is considered in the -dimensional projective space . Principal fiber bundle of tangent linear frames is arised above this manifold. Typical fiber of the principal fiber bundle is the linear group working in the tangent space to the Grassmann manifold. Neifeld’s connection is given in this fibering. It is proved by Cartan’s external forms method, that Bortolotti’s clothing of the Grassmann manifold induces this connection
Classification of (1,2)-Grassmann secant defective threefolds
No full textWe classify all smooth threefolds X in P^N , for which the Grassmann secant variety G(1;2) (i.e. the closure of the set of lines contained in the span of 3 independent points of X) has not the expected dimension
Determination of Grassmann manifolds which are boundaries
No full textLet FGnk denote the Grassmann manifold of all k-dimensional (left) F-vector subspace of Fn for F = R, the reals, C, the complex numbers, or H the quaternions. The problem of determining which of the
Grassmannians bound was addressed by the author in [4]. Partial results were obtained in [4] for the case F = R, including a sufficient condition, due to A. Dold, on n and k for R Gnk to bound. Here, we show that Dold's condition is also necessary, and obtain a new proof of sufficiency using the methods of this paper, which cover the complex and quaternionic cases as well
Grassmann varieties
No full textIn this thesis we study the simplest types of generalized Grassmann varieties. The study involves defining those varieties, understanding their local structures, calculating their Zeta functions, defining cycles on those varieties and studying their cohomology groups.We begin with the classical Grassmannian G( d, n) and then study a special type of the Grassmannian, namely the Lagrangian Grassmannian. For a field k and a subring R ⊂ End(kn) we study the generalized Grassmann variety G(R; d, n) which is the set of all d-dimensional subspaces of kn that are preserved under R. We study the local structure of the generalized Grassmann scheme F R := G(R; d, n) and its zeta function in some particular cases. We study closely the example of a quadratic field when R is the ring of integers
Schubert unions in Grassmann varieties
No full textAbstractWe study subsets of Grassmann varieties G(l,m) over a field F, such that these subsets are unions of Schubert cycles, with respect to a fixed flag. We study unions of Schubert cycles of Grassmann varieties G(l,m) over a field F. We compute their linear span and, in positive characteristic, their number of Fq-rational points. Moreover, we study a geometric duality of such unions, and give a combinatorial interpretation of this duality. We discuss the maximum number of Fq-rational points for Schubert unions of a given spanning dimension, and as an application to coding theory, we study the parameters and support weights of the well-known Grassmann codes. Moreover, we determine the maximum Krull dimension of components in the intersection of G(l,m) and a linear space of given dimension in the Plücker space
On continuous maps between Grassmann manifolds
No full textLet G n,k denote the Grassmann manifold of k-planes in Rn. We show that for any continuous map f: G n,k→Gn,l the induced map inZ/2-cohomology is either zero in positive dimensions or has image in the subring generated by w1(γn, k), provided 1≤l≤k≤[n/2] andn≥k+2l-1. Our main application is to obtain negative results on the existence of equivariant maps between oriented Grassmann manifolds. We also obtain positive results in many cases on the existence of equivariant maps between oriented Grassmann manifolds
Central polynomials for matrix algebras over the Grassmann algebra
No full textIn this work, we describe a method to construct central polynomials for F-algebras where F is a field of characteristic zero. The main application deals with the T-prime algebras Mn(E), where E is the infinite- dimensional Grassmann algebra over F, which play a fundamental role in the theory of PI-algebras. The method is based on the explicit decomposition of the group algebra FSn. AMS Classification 2000: Primary 16R10, Secondary 16W50, 15A75. Keywords: Polynomial identities, central polynomials, Grassmann algebra.
Simple ternary complex Grassmann algebras
No full textThis work introduces a new class of simple comtrans algebras obtained in the tangent space of a complex Grassmann manifold. It is shown that some of the simple algebras of this new, Grassmann type do not appear as simple algebras of any of the previously known types. In chapter one, comtrans algebras are defined and examples given for the four broad types of simple comtrans algebras currently known. Some of the prerequisite details of the general algebraic theory of comtrans algebras, particularly concerning the universal enveloping algebra of a comtrans algebra, are summarized. In chapter two we define a new class of comtrans algebras. The algebras are said to be of complex Grassmann type. We discuss their simplicity and show that each algebra in this class is an internal Thomas sum of its subalgebras E and F defined in the chapter. Chapter three is devoted to the problem of showing that the complex Grassmann comtrans algebras are not isomorphic to other types of simple comtrans algebras, and in conclusion we outline a few conjectures as open problems for further research.</p
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