Special Grassmann manifolds $V ^4 _3$ in the projective space $P _7$

Josef Vala

Displaying similar documents to “Special Grassmann manifolds $V_{3}^{4}$ in the projective space $P_{7}$ ”

The projective limit of the $H^{p}$ spaces

J. A. Cima, J. R. Harrington, J. A. Pfaltzgraff (1977)

Colloquium Mathematicae

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Projective invariant metrics and open convex regular cones. I

Fabio Podestà (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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In this work we give a characterization of the projective invariant pseudometric $P$ , introduced by H. Wu, for a particular class of real $\mathbf{C}^{\infty}$ -manifolds; in view of this result, we study the group of projective transformations for the same class of manifolds and we determine the integrated pseudodistance $p$ of $P$ in open convex regular cones of $\mathbb{R}^{n}$ , endowed with the characteristic metric.

A Note on Lax Projective Embeddings of Grassmann Spaces

Eva Ferrara Dentice (2018)

Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche

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In the paper (Ferrara Dentice et al., 2004) a complete exposition of the state of the art for lax embeddings of polar spaces of ﬁnite rank $\geq 3$ is presented. As a consequence, we have that if a Grassmann space $G$ of dimension 3 and index 1 has a lax embedding in a projective space over a skew–ﬁeld $K$ , then $G$ is the Klein quadric deﬁned over a subﬁeld of $K$ . In this paper, I examine Grassmann spaces of arbitrary dimension $d\geq 3$ and index $h\geq 1$ having a lax embedding in a projective space.

Projective invariant metrics and open convex regular cones. I

Fabio Podestà (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Characterizing projective general unitary groups ${PGU}_{3} (q^{2})$ by their complex group algebras

Farrokh Shirjian, Ali Iranmanesh (2017)

Czechoslovak Mathematical Journal

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Let $G$ be a finite group. Let $X_{1} (G)$ be the first column of the ordinary character table of $G$ . We will show that if $X_{1} (G) = X_{1} ({PGU}_{3} (q^{2}))$ , then $G ≅ {PGU}_{3} (q^{2})$ . As a consequence, we show that the projective general unitary groups ${PGU}_{3} (q^{2})$ are uniquely determined by the structure of their complex group algebras.

Some isomorphic properties in projective tensor products

Ioana Ghenciu (2022)

Commentationes Mathematicae Universitatis Carolinae

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We give sufficient conditions implying that the projective tensor product of two Banach spaces $X$ and $Y$ has the $p$ -sequentially Right and the $p$ - $L$ -limited properties, $1 \leq p < \infty$ .

Grassmann manifold $V_{3}^{4}$ in the projective space $P_{7}$ with characteristics consisting of a quadric and two planes

Josef Vala (1993)

Mathematica Bohemica

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Some results in the geometry of four-parametric manifolds of three-dimensional spaces in the projective space $P_{7}$ are found. The properties of such a manifold $V_{3}^{4}$ with characteristics consisting of a quadric and two planes are studied. The properties of the manifold dual to $V_{3}^{4}$ are found. Some results in the geometry of linear spaces from [1],[2],[3],[4] are used. The notation of the quantities is the same as in [4].

Ding projective and Ding injective modules over trivial ring extensions

Lixin Mao (2023)

Czechoslovak Mathematical Journal

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Let $R ⋉ M$ be a trivial extension of a ring $R$ by an $R$ - $R$ -bimodule $M$ such that $M_{R}$ , $_{R} M$ , ${(R, 0)}_{R ⋉ M}$ and $_{R ⋉ M} (R, 0)$ have finite flat dimensions. We prove that $(X, α)$ is a Ding projective left $R ⋉ M$ -module if and only if the sequence $M \otimes_{R} M \otimes_{R} X \overset{M \otimes α}{⟶} M \otimes_{R} X \overset{α}{\to} X$ is exact and $coker (α)$ is a Ding projective left $R$ -module. Analogously, we explicitly describe Ding injective $R ⋉ M$ -modules. As applications, we characterize Ding projective and Ding injective modules over Morita context rings with zero bimodule homomorphisms.

The reciprocal Dunford–Pettis property of order $p$ in projective tensor products

Ioana Ghenciu (2019)

Commentationes Mathematicae Universitatis Carolinae

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We investigate whether the projective tensor product of two Banach spaces $X$ and $Y$ has the reciprocal Dunford–Pettis property of order $p$ , $1 \leq p < \infty$ , when $X$ and $Y$ have the respective property.

Rings whose nonsingular right modules are $R$ -projective

Yusuf Alagöz, Sinem Benli, Engin Büyükaşık (2021)

Commentationes Mathematicae Universitatis Carolinae

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A right $R$ -module $M$ is called $R$ -projective provided that it is projective relative to the right $R$ -module $R_{R}$ . This paper deals with the rings whose all nonsingular right modules are $R$ -projective. For a right nonsingular ring $R$ , we prove that $R_{R}$ is of finite Goldie rank and all nonsingular right $R$ -modules are $R$ -projective if and only if $R$ is right finitely $Σ$ - $C S$ and flat right $R$ -modules are $R$ -projective. Then, $R$ -projectivity of the class of nonsingular injective right modules is also considered....

Homological dimensions for endomorphism algebras of Gorenstein projective modules

Aiping Zhang, Xueping Lei (2024)

Czechoslovak Mathematical Journal

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Let $A$ be a CM-finite Artin algebra with a Gorenstein-Auslander generator $E$ , $M$ be a Gorenstein projective $A$ -module and $B = {End}_{A} M$ . We give an upper bound for the finitistic dimension of $B$ in terms of homological data of $M$ . Furthermore, if $A$ is $n$ -Gorenstein for $2 \leq n < \infty$ , then we show the global dimension of $B$ is less than or equal to $n$ plus the $B$ -projective dimension of ${Hom}_{A} (M, E) .$ As an application, the global dimension of ${End}_{A} E$ is less than or equal to $n$ .

Generic representations of orthogonal groups: projective functors in the category $ℱ_{q u a d}$

Christine Vespa (2008)

Fundamenta Mathematicae

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We continue the study of the category of functors $ℱ_{q u a d}$ , associated to ₂-vector spaces equipped with a nondegenerate quadratic form, initiated in J. Pure Appl. Algebra 212 (2008) and Algebr. Geom. Topology 7 (2007). We define a filtration of the standard projective objects in $ℱ_{q u a d}$ ; this refines to give a decomposition into indecomposable factors of the first two standard projective objects in $ℱ_{q u a d}$ : $P_{H ₀}$ and $P_{H ₁}$ . As an application of these two decompositions, we give a complete description of the polynomial...

Coloring ordinals by reals

Jörg Brendle, Sakaé Fuchino (2007)

Fundamenta Mathematicae

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We study combinatorial principles we call the Homogeneity Principle HP(κ) and the Injectivity Principle IP(κ,λ) for regular κ > ℵ₁ and λ ≤ κ which are formulated in terms of coloring the ordinals < κ by reals. These principles are strengthenings of $C^{s} (κ)$ and $F^{s} (κ)$ of I. Juhász, L. Soukup and Z. Szentmiklóssy. Generalizing their results, we show e.g. that IP(ℵ₂,ℵ₁) (hence also IP(ℵ₂,ℵ₂) as well as HP(ℵ₂)) holds in a generic extension of a model of CH by Cohen forcing, and IP(ℵ₂,ℵ₂) (hence...

One-sided Gorenstein subcategories

Weiling Song, Tiwei Zhao, Zhaoyong Huang (2020)

Czechoslovak Mathematical Journal

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We introduce the right (left) Gorenstein subcategory relative to an additive subcategory $𝒞$ of an abelian category $𝒜$ , and prove that the right Gorenstein subcategory $r 𝒢 (𝒞)$ is closed under extensions, kernels of epimorphisms, direct summands and finite direct sums. When $𝒞$ is self-orthogonal, we give a characterization for objects in $r 𝒢 (𝒞)$ , and prove that any object in $𝒜$ with finite $r 𝒢 (𝒞)$ -projective dimension is isomorphic to a kernel (or a cokernel) of a morphism from an object in $𝒜$ with finite $𝒞$ -projective...

The classical subspaces of the projective tensor products of $ℓ_{p}$ and C(α) spaces, α < ω₁

Elói Medina Galego, Christian Samuel (2013)

Studia Mathematica

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We completely determine the $ℓ_{q}$ and C(K) spaces which are isomorphic to a subspace of $ℓ_{p} \otimes ̂_{π} C (α)$ , the projective tensor product of the classical $ℓ_{p}$ space, 1 ≤ p < ∞, and the space C(α) of all scalar valued continuous functions defined on the interval of ordinal numbers [1,α], α < ω₁. In order to do this, we extend a result of A. Tong concerning diagonal block matrices representing operators from $ℓ_{p}$ to ℓ₁, 1 ≤ p < ∞. The first main theorem is an extension of a result of E. Oja and states...

Displaying similar documents to “Special Grassmann manifolds V 3 4 in the projective space P 7 ”

Displaying similar documents to “Special Grassmann manifolds $V_{3}^{4}$ in the projective space $P_{7}$ ”