Academic literature on the topic 'Braided crossed module'

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Journal articles on the topic "Braided crossed module"

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Noohi, Behrang. "Group cohomology with coefficients in a crossed module." Journal of the Institute of Mathematics of Jussieu 10, no. 2 (2010): 359–404. http://dx.doi.org/10.1017/s1474748010000186.

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AbstractWe compare three different ways of defining group cohomology with coefficients in a crossed module: (1) explicit approach via cocycles; (2) geometric approach via gerbes; (3) group theoretic approach via butterflies. We discuss the case where the crossed module is braided and the case where the braiding is symmetric. We prove the functoriality of the cohomologies with respect to weak morphisms of crossed modules and also prove the ‘long’ exact cohomology sequence associated to a short exact sequence of crossed modules and weak morphisms.
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Davydov, Alexei, and Dmitri Nikshych. "The Picard crossed module of a braided tensor category." Algebra & Number Theory 7, no. 6 (2013): 1365–403. http://dx.doi.org/10.2140/ant.2013.7.1365.

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Shi, Gui-Qi, Xiao-Li Fang, and Blas Torrecillas. "Generalized Yetter–Drinfeld (quasi)modules and Yetter–Drinfeld–Long bi(quasi)modules for Hopf quasigroups." Journal of Algebra and Its Applications 18, no. 02 (2019): 1950034. http://dx.doi.org/10.1142/s0219498819500348.

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As generalizations of Yetter–Drinfeld module over a Hopf quasigroup, we introduce the notions of Yetter–Drinfeld–Long bimodule and generalize the Yetter–Drinfeld module over a Hopf quasigroup in this paper, and show that the category of Yetter–Drinfeld–Long bimodules [Formula: see text] over Hopf quasigroups is braided, which generalizes the results in Alonso Álvarez et al. [Projections and Yetter–Drinfeld modules over Hopf (co)quasigroups, J. Algebra 443 (2015) 153–199]. We also prove that the category of [Formula: see text] having all the categories of generalized Yetter–Drinfeld modules [Fo
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Ma, Tianshui, Linlin Liu та Haiying Li. "A class of braided monoidal categories via quasitriangular Hopf π-crossed coproduct algebras". Journal of Algebra and Its Applications 14, № 02 (2014): 1550010. http://dx.doi.org/10.1142/s0219498815500103.

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Let π be a group and (H = {Hα}α∈π, μ, η) a Hopf π-algebra. First, we introduce the concept of quasitriangular Hopf π-algebra, and then prove that the left H-π-module category [Formula: see text], where (H, R) is a quasitriangular Hopf π-algebra, is a braided monoidal category. Second, we give the construction of Hopf π-crossed coproduct algebra [Formula: see text]. At last, the necessary and sufficient conditions for [Formula: see text] to be a quasitriangular Hopf π-algebra are derived, and in this case, [Formula: see text] is a braided monoidal category.
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Yan, Dongdong, and Shuanhong Wang. "Drinfel’d construction for Hom–Hopf T-coalgebras." International Journal of Mathematics 31, no. 08 (2020): 2050058. http://dx.doi.org/10.1142/s0129167x20500585.

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Let [Formula: see text] be a Hom–Hopf T-coalgebra over a group [Formula: see text] (i.e. a crossed Hom–Hopf [Formula: see text]-coalgebra). First, we introduce and study the left–right [Formula: see text]-Yetter–Drinfel’d category [Formula: see text] over [Formula: see text], with [Formula: see text], and construct a class of new braided T-categories. Then, we prove that a Yetter–Drinfel’d module category [Formula: see text] is a full subcategory of the center [Formula: see text] of the category of representations of [Formula: see text]. Next, we define the quasi-triangular structure of [Formu
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Ma, Tianshui, and Huihui Zheng. "An extended form of Majid’s double biproduct." Journal of Algebra and Its Applications 16, no. 04 (2017): 1750061. http://dx.doi.org/10.1142/s021949881750061x.

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Let [Formula: see text] be a bialgebra. Let [Formula: see text] be a linear map, where [Formula: see text] is a left [Formula: see text]-module algebra, and a coalgebra with a left [Formula: see text]-weak coaction. Let [Formula: see text] be a linear map, where [Formula: see text] is a right [Formula: see text]-module algebra, and a coalgebra with a right [Formula: see text]-weak coaction. In this paper, we extend the construction of two-sided smash coproduct to two-sided crossed coproduct [Formula: see text]. Then we derive the necessary and sufficient conditions for two-sided smash product
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Iğde, Elif, and Koray Yılmaz. "Tensor Products and Crossed Differential Graded Lie Algebras in the Category of Crossed Complexes." Symmetry 15, no. 9 (2023): 1646. http://dx.doi.org/10.3390/sym15091646.

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The study of algebraic structures endowed with the concept of symmetry is made possible by the link between Lie algebras and symmetric monoidal categories. This relationship between Lie algebras and symmetric monoidal categories is useful and has resulted in many areas, including algebraic topology, representation theory, and quantum physics. In this paper, we present analogous definitions for Lie algebras within the framework of whiskered structures, bimorphisms, crossed complexes, crossed differential graded algebras, and tensor products. These definitions, given for groupoids in existing li
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Fernández-Fariña, A., and M. Ladra. "Braiding for categorical algebras and crossed modules of algebras I: Associative and Lie algebras." Journal of Algebra and Its Applications 19, no. 09 (2019): 2050176. http://dx.doi.org/10.1142/s0219498820501765.

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In this paper, the categories of braided categorical associative algebras and braided crossed modules of associative algebras are studied. These structures are also correlated with the categories of braided categorical Lie algebras and braided crossed modules of Lie algebras.
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Fernández-Fariña, Alejandro, and Manuel Ladra. "Braiding for categorical algebras and crossed modules of algebras II: Leibniz algebras." Filomat 34, no. 5 (2020): 1443–69. http://dx.doi.org/10.2298/fil2005443f.

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In this paper, we study the category of braided categorical Leibniz algebras and braided crossed modules of Leibniz algebras, and we relate these structures with the categories of braided categorical Lie algebras and braided crossed modules of Lie algebras using the Loday-Pirashvili category.
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Arvasi, Z., M. Koçak, and E. Ulualan. "BRAIDED CROSSED MODULES AND REDUCED SIMPLICIAL GROUPS." Taiwanese Journal of Mathematics 9, no. 3 (2005): 477–88. http://dx.doi.org/10.11650/twjm/1500407855.

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Dissertations / Theses on the topic "Braided crossed module"

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PIZZAMIGLIO, LINDA. "Cohomologies of crossed modules." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2014. http://hdl.handle.net/10281/50169.

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Book chapters on the topic "Braided crossed module"

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Natarajan, Elango, Muhammad Rusydi Muhammad Razif, AAM Faudzi, and Palanikumar K. "Evaluation of a Suitable Material for Soft Actuator Through Experiments and FE Simulations." In Research Anthology on Cross-Disciplinary Designs and Applications of Automation. IGI Global, 2022. http://dx.doi.org/10.4018/978-1-6684-3694-3.ch018.

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Soft actuators are generally built to achieve extension, contraction, curling, or bending motions needed for robotic or medical applications. It is prepared with a cylindrical tube, braided with fibers that restrict the radial motion and produce the extension, contraction, or bending. The actuation is achieved through the input of compressed air with a different pressure. The stiffness of the materials controls the magnitude of the actuation. In the present study, Silastic-P1 silicone RTV and multi-wall carbon nanotubes (MWCNT) with reinforced silicone are considered for the evaluation. The dumbbell samples are prepared from both materials as per ASTM D412-06a (ISO 37) standard and their corresponding tensile strength, elongation at break, and tensile modulus are measured. The Ogden nonlinear material constants of respective materials are estimated and used further in the finite element analysis of extension, contraction, and bending soft actuators. It is observed that silicone RTV is better in high strain and fast response, whereas, silicone/MWCNT is better at achieving high actuation.
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Conference papers on the topic "Braided crossed module"

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Bogdanovich, Alexander, and Dmitri Mungalov. "A Novel 3-D Braiding Technology, Complex Shape Preforms and Composites." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-39478.

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A brief overview of 3-D braiding technology and its two major branches, “row and column” and “rotary” braiding, opens the paper. An innovative 3-D braiding process that has been recently patented and implemented in a fully automated multi-modular industrial scale machine is introduced next. The machine enables producing complex, continuously variable shape preforms for composite structures. Each module of the machine incorporates some number of horngears with four yarn carriers placed on each of them. A novel gate switch mechanism, based on the gripping fork controlled rotation, provides smoot
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Shen, Xiuli, and Longdong Gong. "Numerical Modeling of Braided Composites Using Energy Method." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-39619.

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Based on the braiding process and force analysis of yarn, a mesoscopic numerical modeling approach was established, which divided the modeling process as follows: establishing the control points according to the braiding process, establishing the fixed points during jamming, adjusting the control points after jamming, changing the position of fiber bundle due to the fiber bundle intertwined each other and establishing the fiber bundle trajectory according to the minimum strain energy. In the process of adjusting the intertwined fiber bundle trajectories, the fiber bundle trajectory was scatter
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Peel, Larry D., Enrique Molina, Jeff Baur, and Ryan Justice. "Characterization of Shape-Changing Panels With Embedded Rubber Muscle Actuators." In ASME 2012 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/smasis2012-8088.

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There is great interest in making shape-changing aircraft structures that are more biomimetic. Cylindrical McKibben-like flexible actuators efficiently convert fluid pressure into mechanical energy and thus offer excellent force-to-weight ratios while behaving similar to biological muscle. McKibben-like Rubber Muscle Actuators (RMAs) were embedded into elastomer panels. The effect of actuator spacing on the performance of these shape-changing panels was investigated. The work included nonlinear finite element analysis, fabrication, and testing of panels where four RMAs were spaced side-by-side
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