Results 21 to 30 of about 1,060 (95)
Fortschritte der Physik, Volume 69, Issue 7, July 2021., 2021 Abstract The history of the geometry of Double Field Theory is the history of string theorists' effort to tame higher geometric structures. In this spirit, the first part of this paper will contain a brief overview on the literature of geometry of DFT, focusing on the attempts of a global description. In [1] we proposed that the global doubled space is
Luigi Alfonsi
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Weak Hopf Algebra and Its Quiver Representation
Mathematical Problems in Engineering, Volume 2021, Issue 1, 2021., 2021 This study induced a weak Hopf algebra from the path coalgebra of a weak Hopf quiver. Moreover, it gave a quiver representation of the said algebra which gives rise to the various structures of the so‐called weak Hopf algebra through the quiver. Furthermore, it also showed the canonical representation for each weak Hopf quiver.
Muhammad Naseer Khan +5 more
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Right product quasigroups and loops
, 2009 15 pages; v2: minor corrections to author ...
Phillips, J D, Krapez, A, Kinyon, M K
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Topology of quasi divisor graphs associated with non-associative algebra
Ain Shams Engineering JournalThe visualization of graphs representing algebraic structures has increasingly gained traction in chemical engineering research, emerging as a significant scientific challenge in contemporary studies.
Muhammad Nadeem +4 more
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Distributive and trimedial quasigroups of order 243
, 2016 We enumerate three classes of non-medial quasigroups of order $243=3^5$ up to isomorphism. There are $17004$ non-medial trimedial quasigroups of order $243$ (extending the work of Kepka, B\'en\'eteau and Lacaze), $92$ non-medial distributive quasigroups ...
Jedlička, Přemysl +2 more
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Integrally closed and complete ordered quasigroups and loops [PDF]
Proceedings of the American Mathematical Society, 1972 We generalize the well-known results on embedding a partially ordered group in its Dedekind extension by showing that, with the appropriate definition of integral closure, any partially ordered quasigroup (loop) G can be embedded in a complete partially ordered quasigroup (loop) if and only if G is integrally closed.
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Topological Aspects of Quadratic Graphs and M‐Polynomials Utilizing Classes of Finite Quasigroups
Journal of Mathematics, Volume 2026, Issue 1, 2026.Material science, drug design and toxicology studies, which relate a molecule’s structure to its numerous properties and activities, are studied with the use of the topological index. Graphs with finite algebraic structure find extensive applications in fields such as mathematics, elliptic curve cryptography, physics, robotics and information theory ...
Mohammad Mazyad Hazzazi +5 more
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Quasigroups, Loops, and Associative Laws
Journal of Algebra, 1996 The author investigates the question of which weakenings of the associative law imply that a quasigroup is a loop. In particular, he completely settles the question for all laws which are written with four variables, three of which are distinct (``size four laws''). In earlier work [J. Algebra 183, No.
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Quasigroups and Related Systems, 2023 This paper introduced a condition called $\mathcal{R}$-condition under which $(r,s,t)$-inverse quasigroups are universal. Middle isotopic $(r,s,t)$-inverse loops, satisfying the $\mathcal{R}$-condition and possessing a trivial set of $r$-weak inverse permutations were shown to be isomorphic; isotopy-isomorphy for $(r,s,t)$-inverse loops.
Richard Ilemobade +2 more
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On a “grouplike” family of quasigroups
Examples and CounterexamplesQuasigroups are algebraic structures in which divisibility is always defined. This paper illustrates some similarities and differences between quasigroup theory and group theory, by singling out a special family of quasigroups which seem to be most ...
Ahmed Al Fares, Gizem Karaali
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