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Relevant bibliographies by topics / Braided crossed module

Academic literature on the topic 'Braided crossed module'

Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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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 (June 17, 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 (September 19, 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 (February 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 [Formula: see text], [Formula: see text] as components is a crossed [Formula: see text]-category.

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Ma, Tianshui, Linlin Liu, and Haiying Li. "A class of braided monoidal categories via quasitriangular Hopf π-crossed coproduct algebras." Journal of Algebra and Its Applications 14, no. 02 (October 19, 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 (June 23, 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 [Formula: see text] and show that the representation crossed category [Formula: see text] is quasi-braided. Finally, the Drinfel’d construction [Formula: see text] of [Formula: see text] is constructed, and an equivalent relation between [Formula: see text] and the representation of [Formula: see text] is given.

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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 (April 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 algebra [Formula: see text] and [Formula: see text] to be a bialgebra, which generalizes the Majid’s double biproduct in [Double-bosonization of braided groups and the construction of [Formula: see text], Math. Proc. Camb. Philos. Soc. 125(1) (1999) 151–192] and the Wang–Wang–Yao’s crossed coproduct in [Hopf algebra structure over crossed coproducts, Southeast Asian Bull. Math. 24(1) (2000) 105–113].

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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 (September 27, 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 (September 2005): 477–88. http://dx.doi.org/10.11650/twjm/1500407855.

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Quang, N. T., C. T. K. Phung, and P. T. Cuc. "Braided equivariant crossed modules and cohomology of Γ-modules." Indian Journal of Pure and Applied Mathematics 45, no. 6 (December 2014): 953–75. http://dx.doi.org/10.1007/s13226-014-0098-z.

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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, 339–53. 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 smooth transfer of yarn carriers between adjacent horngears. Each gripping fork is controlled individually, thus allowing fabricating practically unlimited variety of complex cross section 3-D braided preforms. Examples of manufactured braided products include rectangular bars, T-, I- and J-stiffeners, box-beams, hollow tubes, etc. Results and discussion of mechanical characterization of 3-D braided carbon and E-glass composites conclude the paper.

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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 scattered. Using extrapolation adjustment method, discrete points of fiber bundle trajectory intertwined were adjusted in turn from the control points to the fixed points. Adjusted discrete points were equivalent at the corresponding location points of the corresponding trajectory, and at the same time, there was non-interference between the fiber bundle trajectories. Using this method, fiber bundle trajectory and cross section of the models of 2-D woven and 3-D four-directional braided composite materials were established, compared with the experiment result, which were consistent with the electronic microscope scan images and calculated woven structure size was in agreement with the measured data. The maximum relative calculation error of braiding bitch of 3-D four-directional braided structure was about 5%, especially braiding angle was 21° or so, the relative calculation error was below 2%. The maximum relative calculation error of surface braiding angle of 3-D four-directional braided structure was about 4%, especially braiding angle was 21° or so, the relative calculation error was below 2.4%. This modeling approach was fundamental for further analysis of the micromechanical strength and life of braided composites, which was applied to aero-engine hot section.

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Roche, Ellen T., Markus A. Horvath, Ali Alazmani, Kevin C. Galloway, Nikolay V. Vasilyev, David J. Mooney, Frank A. Pigula, and Conor J. Walsh. "Design and Fabrication of a Soft Robotic Direct Cardiac Compression Device." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47355.

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A direct cardiac compression (DCC) device is an active sleeve that is surgically placed around the heart to help the failing heart to pump without contacting blood. Soft robotic techniques enable fabrication of a conformable DCC device containing modular actuators oriented in a biomimetic manner that can restore the natural motion of the heart and provide tunable active assistance. In this paper we describe the fabrication of a DCC device; the optimization of pneumatic actuators, their integration into a matrix with a modulus in the range of cardiac tissue and methods to affix this device to the heart wall. Pneumatic air muscles (PAMs) were fabricated using a modified McKibben technique and four types of internal bladders; low durometer silicone tubes molded in-house, polyester terephthalate (PET) heat shrink tubing, nylon medical balloons and thermoplastic urethane (TPU) balloons thermally formed in-house. Balloons were bonded to air supply lines, placed inside a braided nylon mesh with a 6.35mm resting diameter and bonded at one end. When pressurized to 145kPa silicone tubes failed and PET, nylon and TPU actuators generated isometric axial forces of 14.28, 19.65 and 19.05N respectively, with axial contractions of 33.11, 28.69 and 37.54%. Circumferential actuators placed around the heart reduced the cross-sectional area by 33.34% and 50.63% for silicone and TPU actuators respectively. PAMs were integrated into a soft matrix in a biomimetic orientation using three techniques; casting, thermal forming and layering. Designs were compared on an in vitro cardiac simulator and generated a volumetric displacement of up to 96ml when actuated for 200ms at 1Hz. Layering produced the lowest profile device that successfully conformed to the heart and this design is currently undergoing in vivo testing.

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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, 1/2, 1, and 1.3 RMA diameters apart. Nonlinear “Laminated Plate” and “Rod & Plate” finite element models of individual RMAs were created from existing RMA dimensions. After adjusting for an initial “activation pressure,” the models produced realistic RMA forces. The laminated plate models used less computer resources, but only produced small amounts of actuator contraction (actuator strain). The more resource-intensive Rod & Plate models better replicated fiber/braid re-orientation and produced axial strains up to 60% of test values. Three types of embedded RMA panel FEA models; a “2D Cross-Section,” a “Full 3D Panel” (with either Laminated Plate or Rod & Plate RMAs) and a “3D Unit Cell” (also with either Laminated Plate or Rod & Plate RMAs). The Full 3D Rod & Plate model gave the most accurate strains and forces, but required unsustainable levels of computing resources. The 2D cross-section model predicted optimal RMA spacing to be at 1 diameter. All other FEA models show optimal panel performance between 1/2 and 1 diameter spacing. Panels with embedded RMAs were fabricated and tested with air or water pressure. Panel force as a function of pressure and as a function of contraction (strain) was obtained. Overall, FEA and test results for panels indicate that optimal performance occurs when the RMAs are spaced between 1/2 to 1 diameter apart. Actuator force as a function of spacing is fairly flat in this region, indicating that minor design or manufacturing differences may not significantly affect performance. However, the total amount of axial contraction decreases significantly at greater than optimal spacing. Useful design, simulation, and test methodologies for embedded RMA panels have been demonstrated.

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