Let $\Lambda=\left(\begin{smallmatrix} A&M 0&B \end{smallmatrix}\right)$ be an Artin algebra. In view of the characterization of finitely generated Gorenstein injective $\Lambda$-modules under the condition that $M$ is a cocompatible $(A,B)$-bimodule, we establish a recollement of the stable category $\overline{\rm Ginj(\Lambda)}$. We also determine all strongly complete injective resolutions and all strongly Gorenstein injective modules over $\Lambda$., Chao Wang, Xiaoyan Yang., and Obsahuje bibliografii
The relative cohomology Hdiff1(K(1|3), osp(2, 3);Dγ,µ(S1|3)) of the contact Lie superalgebra K(1|3) with coefficients in the space of differential operators Dγ,µ(S1|3) acting on tensor densities on S1|3, is calculated in N.Ben Fraj, I. Laraied, S. Omri (2013) and the generating 1-cocycles are expressed in terms of the infinitesimal super-Schwarzian derivative 1-cocycle s(Xf) = D1D2D3(f)α31/2, Xf \in K(1|3) which is invariant with respect to the conformal subsuperalgebra osp(2, 3) of K(1|3). In this work we study the supergroup case. We give an explicit construction of 1-cocycles of the group of contactomorphisms K(1|3) on the supercircle S1|3 generating the relative cohomology Hdiff1(K(1|3), PC(2, 3); Dγ,µ(S1|3) with coefficients in Dγ,µ(S1|3). We show that they possess properties similar to those of the super-Schwarzian derivative 1-cocycle S3(Φ) = EΦ-1 (D1(D2),D3)α31/2, Φ ∈ K(1|3) introduced by Radul which is invariant with respect to the conformal group PC(2, 3) of K(1|3). These cocycles are expressed in terms of S3(Φ) and possess its properties., Boujemaa Agrebaoui, Raja Hattab., and Obsahuje seznam literatury
A (0, 2)-graph is a connected graph, where each pair of vertices has either 0 or 2 common neighbours. These graphs constitute a subclass of (0, λ)-graphs introduced by Mulder in 1979. A rectagraph, well known in diagram geometry, is a triangle-free (0, 2)-graph. (0, 2)-graphs include hypercubes, folded cube graphs and some particular graphs such as icosahedral graph, Shrikhande graph, Klein graph, Gewirtz graph, etc. In this paper, we give some local properties of 4-cycles in (0, λ)-graphs and more specifically in (0, 2)-graphs, leading to new characterizations of rectagraphs and hypercubes., Khadra Bouanane, Abdelhafid Berrachedi., and Obsahuje bibliografii
Using a distributional approach to integration in superspace, we investigate a Cauchy-Pompeiu integral formula in super Dunkl-Clifford analysis and several related results, such as Stokes formula, Morera's theorem and Painlevé theorem for super Dunkl-monogenic functions. These results are nice generalizations of well-known facts in complex analysis., Hongfen Yuan., and Obsahuje bibliografické odkazy
In the class of real hypersurfaces M²n−¹ isometrically immersed into a nonflat complex space form Mn(c) of constant holomorphic sectional curvature c (≠ 0) which is either a complex projective space ℂPn(c) or a complex hyperbolic space ℂHn(c) according as c > 0 or c < 0, there are two typical examples. One is the class of all real hypersurfaces of type (A) and the other is the class of all ruled real hypersurfaces. Note that the former example are Hopf manifolds and the latter are non-Hopf manifolds. In this paper, inspired by a simple characterization of all ruled real hypersurfaces in Mn(c), we consider a certain real hypersurface of type (A2) in ℂPn(c) and give a geometric characterization of this Hopf manifold., Byung Hak Kim, In-Bae Kim, Sadahiro Maeda., and Obsahuje bibliografii