Relevant bibliographies by topics / Skew brace

Academic literature on the topic 'Skew brace'

Author: Grafiati
Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Skew brace"

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Rump, Wolfgang. "Set-theoretic solutions to the Yang–Baxter equation, skew-braces, and related near-rings." Journal of Algebra and Its Applications 18, no. 08 (July 5, 2019): 1950145. http://dx.doi.org/10.1142/s0219498819501457.

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Skew-braces have been introduced recently by Guarnieri and Vendramin. The structure group of a non-degenerate solution to the Yang–Baxter equation is a skew-brace, and every skew-brace gives a set-theoretic solution to the Yang–Baxter equation. It is proved that skew-braces arise from near-rings with a distinguished exponential map. For a fixed skew-brace, the corresponding near-rings with exponential form a category. The terminal object is a near-ring of self-maps, while the initial object is a near-ring which gives a complete invariant of the skew-brace. The radicals of split local near-rings with a central residue field [Formula: see text] are characterized as [Formula: see text]-braces with a compatible near-ring structure. Under this correspondence, [Formula: see text]-braces are radicals of local near-rings with radical square zero.
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De Commer, K. "Actions of skew braces and set-theoretic solutions of the reflection equation." Proceedings of the Edinburgh Mathematical Society 62, no. 4 (June 25, 2019): 1089–113. http://dx.doi.org/10.1017/s0013091519000129.

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AbstractA skew brace, as introduced by L. Guarnieri and L. Vendramin, is a set with two group structures interacting in a particular way. When one of the group structures is abelian, one gets back the notion of brace as introduced by W. Rump. Skew braces can be used to construct solutions of the quantum Yang–Baxter equation. In this article, we introduce a notion of action of a skew brace, and show how it leads to solutions of the closely associated reflection equation.
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Catino, Francesco, Ilaria Colazzo, and Paola Stefanelli. "Skew left braces with non-trivial annihilator." Journal of Algebra and Its Applications 18, no. 02 (February 2019): 1950033. http://dx.doi.org/10.1142/s0219498819500336.

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We describe the class of all skew left braces with non-trivial annihilator through ideal extension of a skew left brace. The ideal extension of skew left braces is a generalization to the non-abelian case of the extension of left braces provided by Bachiller in [D. Bachiller, Extensions, matched products, and simple braces, J. Pure Appl. Algebra 222 (2018) 1670–1691].
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Koch, Alan. "Abelian maps, bi-skew braces, and opposite pairs of Hopf-Galois structures." Proceedings of the American Mathematical Society, Series B 8, no. 16 (June 9, 2021): 189–203. http://dx.doi.org/10.1090/bproc/87.

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Let G G be a finite nonabelian group, and let ψ : G → G \psi :G\to G be a homomorphism with abelian image. We show how ψ \psi gives rise to two Hopf-Galois structures on a Galois extension L / K L/K with Galois group (isomorphic to) G G ; one of these structures generalizes the construction given by a “fixed point free abelian endomorphism” introduced by Childs in 2013. We construct the skew left brace corresponding to each of the two Hopf-Galois structures above. We will show that one of the skew left braces is in fact a bi-skew brace, allowing us to obtain four set-theoretic solutions to the Yang-Baxter equation as well as a pair of Hopf-Galois structures on a (potentially) different finite Galois extension.
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Bachiller, David. "Solutions of the Yang–Baxter equation associated to skew left braces, with applications to racks." Journal of Knot Theory and Its Ramifications 27, no. 08 (July 2018): 1850055. http://dx.doi.org/10.1142/s0218216518500554.

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Given a skew left brace [Formula: see text], a method is given to construct all the non-degenerate set-theoretic solutions [Formula: see text] of the Yang–Baxter equation such that the associated permutation group [Formula: see text] is isomorphic, as a skew left brace, to [Formula: see text]. This method depends entirely on the brace structure of [Formula: see text]. We then adapt this method to show how to construct solutions with additional properties, like square-free, involutive or irretractable solutions. Using this result, it is even possible to recover racks from their permutation group.
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Jespers, Eric, and Arne Van Antwerpen. "Left semi-braces and solutions of the Yang–Baxter equation." Forum Mathematicum 31, no. 1 (January 1, 2019): 241–63. http://dx.doi.org/10.1515/forum-2018-0059.

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Abstract Let {r\colon X^{2}\rightarrow X^{2}} be a set-theoretic solution of the Yang–Baxter equation on a finite set X. It was proven by Gateva-Ivanova and Van den Bergh that if r is non-degenerate and involutive, then the algebra {K\langle x\in X\mid xy=uv\text{ if }r(x,y)=(u,v)\rangle} shares many properties with commutative polynomial algebras in finitely many variables; in particular, this algebra is Noetherian, satisfies a polynomial identity and has Gelfand–Kirillov dimension a positive integer. Lebed and Vendramin recently extended this result to arbitrary non-degenerate bijective solutions. Such solutions are naturally associated to finite skew left braces. In this paper we will prove an analogue result for arbitrary solutions {r_{B}} that are associated to a left semi-brace B; such solutions can be degenerate or can even be idempotent. In order to do so, we first describe such semi-braces and then prove some decompositions results extending those of Catino, Colazzo and Stefanelli.
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Nasybullov, Timur. "Connections between properties of the additive and the multiplicative groups of a two-sided skew brace." Journal of Algebra 540 (December 2019): 156–67. http://dx.doi.org/10.1016/j.jalgebra.2019.05.005.

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Bardakov, Valeriy G., Mikhail V. Neshchadim, and Manoj K. Yadav. "Computing skew left braces of small orders." International Journal of Algebra and Computation 30, no. 04 (March 10, 2020): 839–51. http://dx.doi.org/10.1142/s0218196720500216.

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We improve Algorithm 5.1 of [Math. Comp. 86 (2017) 2519–2534] for computing all nonisomorphic skew left braces, and enumerate left braces and skew left braces of orders up to 868 with some exceptions. Using the enumerated data, we state some conjectures for further research.
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Jespers, E., Ł. Kubat, A. Van Antwerpen, and L. Vendramin. "Factorizations of skew braces." Mathematische Annalen 375, no. 3-4 (September 20, 2019): 1649–63. http://dx.doi.org/10.1007/s00208-019-01909-1.

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Bardakov, Valeriy G., Mikhail V. Neshchadim, and Manoj K. Yadav. "On λ-homomorphic skew braces." Journal of Pure and Applied Algebra 226, no. 6 (June 2022): 106961. http://dx.doi.org/10.1016/j.jpaa.2021.106961.

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Dissertations / Theses on the topic "Skew brace"

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CAMPEDEL, ELENA. "Hopf-Galois Structures and Skew Braces of order p^2q." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2022. http://hdl.handle.net/10281/378739.

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Nella mia tesi enumero le strutture Hopf-Galois su estensioni di Galois di ordine p^2q. Questo sarà fatto, mediante l'uso delle funzioni gamma, contando i sottogruppi regolari dell'olomorfo di gruppi di ordine p^2q. Questi ultimi oggetti sono anche connessi con le skew braces, e fornisco anche il numero di classi di isomorfismo di skew braces di ordine p^2q.
In my thesis I enumerate the Hopf-Galois structures on Galois extensions of order p^2q. This will be done, using the gamma functions, by enumerating the regular subgroups of the holomorph of groups G of order p^2q. The last objects are also connected to skew braces, and I also provide the number of isomorphism classes of skew braces of size p^2q.
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Nejabati, Zenouz Kayvan. "On Hopf-Galois structures and skew braces of order p³." Thesis, University of Exeter, 2018. http://hdl.handle.net/10871/32248.

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The concept of Hopf-Galois extensions was introduced by S. Chase and M. Sweedler in 1969 and provides a generalisation of classical Galois theory. Later, Hopf-Galois theory for separable extensions of fields was studied by C. Greither and B. Pareigis. They showed how to recast the problem of classifying all Hopf-Galois structures on a finite separable extension of fields as a problem in group theory. Many major advances relating to the classification of Hopf-Galois structures were made by N. Byott, S. Carnahan, L. Childs, and T. Kohl. On the other hand, and seemingly unrelated to Hopf-Galois theory, in 1992 V. Drinfeld formulated a number of problems in quantum group theory. In particular, he suggested considering set-theoretic solutions of the Yang-Baxter equation. Later, W. Rump introduced braces as a tool to study non-degenerate involutive set-theoretic solutions, and through the efforts of D. Bachiller, F. Ced'o, E. Jespers, and J. Okni'nski the classification of these solutions was reduced to that of braces. Recently, skew braces were introduced by L. Guarnieri and L. Vendramin in order to study the non-degenerate (not necessarily involutive) set-theoretic solutions. Additionally, a fruitful discovery, initially noticed by D. Bachiller, revealed a connection between Hopf-Galois theory and skew braces, which linked the classification of Hopf-Galois structures to that of skew braces. Currently, the classification of Hopf-Galois structures and skew braces of a given order remains among important topics of research. In this thesis, as our main results, we determine all Hopf-Galois structures on Galois extensions of fields of degree p^3, and at the same time we provide a complete classification of all skew braces of order p^3, for a prime number p. These findings hence offer applications to Galois module theory in number theory on the one hand, and to the study of the solutions of the quantum Yang-Baxter equation in mathematical physics on the other hand.
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Bachiller, Pérez David. "Study of the algebraic structure of left braces and the yang-baxter equation." Doctoral thesis, Universitat Autònoma de Barcelona, 2016. http://hdl.handle.net/10803/385215.

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Aquesta tesi doctoral tracta de l’estructura algebraica anomenada braça no commutativa per l’esquerra, i de les seves aplicacions a les solucions conjuntistes no degenerades de l’equació de Yang-Baxter. Concretament, estudiem els següents problemes: (1) Construïm totes les solucions conjuntistes no-degenerades associades a una braça per l’esquerra no commutativa donada. A més, demostrem que totes les solucions no-degenerades involutives es poden construir a partir de braces per l’esquerra amb una construcció similar. Aquests resultats estan continguts als Capítols 2 i 3. Això redueix el problema de la classificació de solucions conjuntistes no-degenerades de l’equació de Yang-Baxter a la classificació de braces per l’esquerra no commutatives, un problema que tractem d’estudiar a la resta de la tesi. (2) A la Secció 4.1, presentem dos mètodes nous per a construir braces per l’esquerra: extensions de braces per l’esquerra per ideals trivials, i matched product de braces. Aquestes construccions estan basades en les construccions anàlogues en grups. (3) Motivats per les extensions de braces, a la Secció 4.2 construïm la primera família de braces per l’esquerra simples no trivials. Per a aconseguir-ho, fem servir la construcció de matched products que havíem definit prèviament. (4) Responent a una pregunta de Cedó, Jespers i del Río, trobem el primer exemple de p-grup finit que no és grup multiplicatiu d’una braça per l’esquerra. Això demostra que no tot grup finit resoluble és grup multiplicatiu d’una braça per l’esquerra. Aquest resultat es troba a la Secció 4.3. (5) Finalment, classifiquem totes les braces per l’esquerra d’ordre p, p^2 i p^3, on p és un primer. Aquest resultat es troba contingut a la Secció 4.4 i al Capítol 5.
This PhD thesis deals with the algebraic structure called non-commutative left brace, and with its applications for the non-degenerate set-theoretic solutions of the Yang-Baxter equation. Concretely, we study the following problems: (1) We construct all the non-degenerate set-theoretic solutions of the Yang-Baxter equation associated with a fixed non-commutative left brace. Moreover, we prove all the non-degenerate involutive solutions can be obtained from left braces with an analogous construction. These results are contained in Chapters 2 and 3. This reduces the problem of classification of non-degenerate set-theoretic solutions of the Yang-Baxter equation to the classification of non-commutative left braces, a problem that we study for the rest of the memoir. (2) In Section 4.1, we present two new methods to construct new left braces: extensions of left braces by trivial ideals, and matched product of left braces. These constructions are based on the analogous constructions of group theory. (3) Motivated by the extensions of left braces, in Section 4.2 we construct the first family of non-trivial simple left braces. We use the matched product method that we have defined previously to obtain this family. (4) Answering a question of Cedó, Jespers and del Río, we find the first exemple of finite p-group which is not the multiplicative group of any left brace. This proves that not all finite solvable groups are multiplicative groups of left braces. This results is contained in Section 4.3. (5) Finally, we classify all the left braces of order p, p^2 and p^3, where p is a prime. This result is contained in Section 4.4 and Chapter 5.
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Book chapters on the topic "Skew brace"

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"Hopf-Galois structures on Galois extensions of fields, regular subgroups, and skew braces." In Mathematical Surveys and Monographs, 13–26. Providence, Rhode Island: American Mathematical Society, 2021. http://dx.doi.org/10.1090/surv/260/02.

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Bennett, Peggy D. "Facing fear." In Teaching with Vitality. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780190673987.003.0020.

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Do you know what you fear? Some folks know the answer right away. Others need to think about it for a while. Fears have a wide range of characteristics. Some fears may serve, others may hamper. What do you do about your fears? How do they affect you? Many of us had a general fear when we began teaching. We may not have been able to identify what or who we were afraid of, but we were afraid. For teachers, fears of embarrassing one­self, of showing others how ill- informed and unprepared we are, and of being unable to “handle” students’ behaviors are com­mon. The very real fear about safety in schools is, sad to say, a potent concern as well. Some believe that systematically dismantling fear helps. Others recommend that copiously proving how silly fears are can relieve us of them. Some believe additional information helps dissolve fears or puts them into perspective. Have you ever considered how it would feel to be fearless? Take a moment to feel totally fearless. Were you able to do it? What would change if you were at school every day without fear? When our state of mind is not shackled by fear, imagine what we could accomplish. Letting fear consume us, no matter how impending we feel the danger to be, can skew our reasoning and taint our percep­tions. Some of us even fear the fear! When Barbara Brown Taylor stated, “We’d like life to be a train, and it’s a sailboat,” she cap­tured the sentiment that we often fall victim to our own fears and anxieties. We would like a straight, predictable path. But we most often get a path that changes when we least expect it, that takes us places we never intended to go. And sometimes those places we go bring us exactly what we need. So, rather than run from our fears, we can face them. Rather than worry, we can be fearless, even if momentarily. Rather than fret, we can calm ourselves. We can take a moment to consider that, beyond our limited vision, all may be well. Take three deep breaths. Face your fear. Stand tall. Be brave.
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Conference papers on the topic "Skew brace"

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Suzuki, Masakuni, Takeshi Ishida, and Shingo Kono. "Vibration Reduction Applying Skew Phenomena of Needle Roller Bearings in Brake Actuators." In SAE 2006 World Congress & Exhibition. 400 Commonwealth Drive, Warrendale, PA, United States: SAE International, 2006. http://dx.doi.org/10.4271/2006-01-0881.

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Pewekar, Mihir Mangesh, Pranit Pravin Sandye, and Kiran Chaudhari. "Investigation of Non-Pneumatic Tires Based on Helical Hexagonal Cellular Structure." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-87631.

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Non-pneumatic tires (NPTs) have drawn attention mainly due to low contact pressure and low rolling resistance due to use of hyper-elastic materials in their construction. In this paper, an attempt to innovate the conventional design of NPT with hexagonal honeycomb cellular structure is made by creating the boundary planar geometries of the tire, skew to each other at a certain angle. Adding to the functionality as a tire, this modified structure increases the performance of automobile components by rejection of heat through convection (forced) at the expense of engine power. The primary investigation includes study of the effects of variation in degree of skewness with the strength and flow of air through the tire. The flow parameters are computed for rotational case and the heat transfer is computed for flow over a brake disk. The secondary investigation consists of finding an optimum range of the degree of skewness. The validation for strength is computed through Finite Element Analysis. The fluid flow is computed through Computational Fluid Dynamics approach in ANSYS Fluent. This modified structure improves the aerodynamic condition near the brake rotor that increases the rate of heat rejection by forced convection from the brake rotor surface.
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Savander, Brant R., Malcolm E. Willis, Karl A. Stambaugh, and Kelley A. Cox. "USCG Patrol Craft Hydrodynamic Fuel Efficiency Improvements." In SNAME 13th International Conference on Fast Sea Transportation. SNAME, 2015. http://dx.doi.org/10.5957/fast-2015-035.

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A computational analysis program, conducted at full scale, has been completed on the USCG Fast Response Cutter (FRC) to evaluate how appendage and propeller redesign affects calm water powering performance and erosive cavitation onset. Aft working forward, the geometric variations considered included: addition of a stern flap, wake adapted rudder redesign, propeller design refinement, wake adapted skeg redesign, and redesign of the spray rail system. The first activity was to use a wake alignment procedure to redesign the current rudder in an effort to improve the rudder drag characteristics and minimize or eliminate rudder cavitation. The wake aligned redesign eliminated rudder cavitation over the entire speed range, and decreased total drag by 6% at flank speed. Replacement of only the current rudders with the wake aligned redesign is predicted to increase flank speed from 28.9 knots to 29.4 knots. The stern flap and spray rail efforts followed the historical guidance of similar work performed on the USCG Island Class patrol boats, as documented in Cusanelli and Barry (2002). Following the geometric guidance of the Island Class stern flaps the final recommended stern flap for the FRC results in a brake power demand reduction of 15%. The Island Class achieved a 12% reduction in required brake power at similar speeds. The combination of the new stern flap, wake adapted rudders, current propeller, current skegs, and new spray rail yielded an increase in flank speed from 28.9 to 31.4 knots. Skeg redesign resulted in a 30% decrease in the magnitude of the radiated pressure pulse amplitudes experienced in the propeller tunnel above the propeller. The redesign of the skeg did not affect the propeller behind efficiency. Modification of the current propeller geometry was the final redesign task. The final system, which included the new stern flap, wake aligned rudders, redesigned propeller, wake aligned skegs, and new spray rail system decreased power by 18.6% at the prior 28.9 knot flank speed of FRC. The new flank speed, with the final system, has increased to 32.9 knots in the full load, end of service life condition. The combined effect of all redesign activities reveals an annual fuel consumption savings of 24,000 gallons per vessel per year, which corresponds to a 13.6% savings when compared to the original as-built system. Assuming a fuel cost of $4 per gallon, the annual cost savings per vessel per year equals $96,000. This savings extrapolated over a 58 ship fleet equates to $5.5 million in savings per year for the class. This saving per year yields a savings of $110 million for the 20-year operating life of the 58-ship class.
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