Results 11 to 20 of about 709,594 (295)
Homology, Homotopy and Applications, 2009 We introduce the notion of 3-crossed module, which extends the notions of 1-crossed module (Whitehead) and 2-crossed module (Conduché). We show that the category of 3-crossed modules is equivalent to the category of simplicial groups having a Moore complex of length 3.
Arvasi, Z. +2 more
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Notices of the American Mathematical Society, 2023 This is an overview of the idea of a crossed module. For a group, the triple that consists of the group, its group of automorphisms, and the canonical homomorphism from the group to its group of automorphisms constitutes a crossed module. Crossed modules arise from the identities among the relations of the presentation of a group, from the extension ...
Huebschmann, Johannes
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Bimultiplications and Annihilators of Crossed Modules in Associative Algebras
Journal of New Theory, 2021 In this paper, we present a generalization of the concept of the bimultiplication algebra by defining the bimultiplication of crossed modules in associative algebras.
Ummahan Ege Arslan, Serdar Hürmetli
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Coproduct of Crossed A-Modules of R-Algebroids
Topological Algebra and its Applications, 2017 In this study we construct, in the category XAlg(R) / A of crossed A-modules of R-algebroids, the coproduct of given two crossed A-modules M = (μ : M → A) and N = (ɳ : N → A) of R-algebroids in two different ways: Firstly we construct the coproduct M ᴼ ...
Avcıoglu Osman, Akça Ibrahim Ilker
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Journal of Symbolic Computation, 2016 We introduce the isoclinism of crossed modules. We also give GAP implementations for constructing the isoclinism families of finite crossed modules and consequently give an enumeration about isoclinic crossed modules existing in the GAP library.
Alper Odabaş
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On Lie Algebra Crossed Modules [PDF]
Communications in Algebra, 2006 This article constructs a crossed module corresponding to the generator of the third cohomology group with trivial coefficients of a complex simple Lie algebra. This generator reads as , constructed from the Lie bracket [,] and the Killing form . The construction is inspired by the corresponding construction for the Lie algebra of formal vector fields ...
Friedrich Wagemann
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Crossed Wavelet Convolution Network for Few-Shot Defect Detection of Industrial Chips [PDF]
SensorsIn resistive polymer humidity sensors, the quality of the resistor chips directly affects the performance. Detecting chip defects remains challenging due to the scarcity of defective samples, which limits traditional supervised-learning methods requiring
Zonghai Sun, Yiyu Lin, Yan Li, Zihan Lin
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Homotopies and Automorphisms of Crossed Modules of Groupoids
Applied Categorical Structures, 2003 We give a detailed description of the structure of the actor 2-crossed module related to the automorphisms of a crossed module of groupoids. This generalises work of Brown and Gilbert for the case of crossed modules of groups, and part of this is needed for work on 2-dimensional holonomy to be developed elsewhere (see math.DG/0009082).
Ronald Brown, İlhan İÇen
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Crossed Modules for Lie 2-Algebras [PDF]
Applied Categorical Structures, 2015 The notion of crossed modules for Lie 2-algebras is introduced. We show that, associated to such a crossed module, there is a strict Lie 3-algebra structure on its mapping cone complex and a strict Lie 2-algebra structure on its derivations. Finally, we classify strong crossed modules by means of the third cohomology group of Lie 2-algebras.
Zhang-Ju Liu
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Higher Chern-Simons-Antoniadis-Savvidy forms based on crossed modules
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy PhysicsWe present higher Chern-Simons-Antoniadis-Savvidy (ChSAS) forms based on crossed modules. We start from introducing a generalized multilinear symmetric invariant polynomial for the differential crossed modules and constructing a metric independent ...
Danhua Song, Ke Wu, Jie Yang
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