Projective invariant metrics and open convex regular cones. I

Fabio Podestà

Displaying similar documents to “Projective invariant metrics and open convex regular cones. I”

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.

Special Grassmann manifolds $V_{3}^{4}$ in the projective space $P_{7}$

Josef Vala (1988)

Časopis pro pěstování matematiky

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

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

Colloquium Mathematicae

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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.

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, $1 \leq p < \infty$ .

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.

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 $n$ .

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...

Fitting Conditions for Symmetric Algebras of Modules of Finite Projective Dimension

Cristodor Ionescu, Gaetana Restuccia, Rosanna Utano (2007)

Bollettino dell'Unione Matematica Italiana

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Let $E$ be a finitely generated $R$ -module, having finite projective dimension. We study the acyclicity of the approximation complex $\mathcal{Z}(E)$ of $E$ in terms of certain Fitting conditions $F_{k}^{(i)}$ on the Fitting ideals of the $i$ -th module of a projective resolution of $E$ . We deduce some good properties of the symmetric algebra of $E$ .

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...

A Regular Threefold of General Type with $p_{g}=0$ and $P_{2}=6$

M. Cristina Ronconi (2009)

Bollettino dell'Unione Matematica Italiana

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The range of the bigenus $P_{2}$ is one of the unsolved problems concerning smooth complex projective regular threefolds of general type with $p_{g}=0$ : The examples in the literature have $P_{2}\leq 5$ . In the present paper we present a non-singular threefold with $p_{g}=q_{1}=q_{2}=0$ ; $P_{2}=6$ ; the bicanonical map is stably birational.

Monodromy of a family of hypersurfaces

Vincenzo Di Gennaro, Davide Franco (2009)

Annales scientifiques de l'École Normale Supérieure

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Let $Y$ be an $(m + 1)$ -dimensional irreducible smooth complex projective variety embedded in a projective space. Let $Z$ be a closed subscheme of $Y$ , and $δ$ be a positive integer such that $ℐ_{Z, Y} (δ)$ is generated by global sections. Fix an integer $d \geq δ + 1$ , and assume the general divisor $X \in | H^{0} (Y, ℐ_{Z, Y} (d)) |$ is smooth. Denote by $H^{m} {(X; ℚ)}_{⊥ Z}^{van}$ the quotient of $H^{m} (X; ℚ)$ by the cohomology of $Y$ and also by the cycle classes of the irreducible components of dimension $m$ of $Z$ . In the present paper we prove that the monodromy representation on $H^{m} {(X; ℚ)}_{⊥ Z}^{van}$ for the family...

Finite projective planes, Fermat curves, and Gaussian periods

Koen Thas, Don Zagier (2008)

Journal of the European Mathematical Society

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One of the oldest and most fundamental problems in the theory of finite projective planes is to classify those having a group which acts transitively on the incident point-line pairs (flags). The conjecture is that the only ones are the Desarguesian projective planes (over a finite field). In this paper, we show that non-Desarguesian finite flag-transitive projective planes exist if and only if certain Fermat surfaces have no nontrivial rational points, and formulate several other equivalences...