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Keywords = superhyperstructure

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28 pages, 338 KB  
Article
Superhypermagma, Lie Superhypergroup, Quotient Superhypergroups, and Reduced Superhypergroups
by Takaaki Fujita
Int. J. Topol. 2025, 2(3), 10; https://doi.org/10.3390/ijt2030010 - 8 Jul 2025
Viewed by 769
Abstract
Classical algebraic structures—such as magmas, groups, and Lie groups—are characterized by increasingly strong requirements in binary operation, ranging from no additional constraints to associativity, identity, inverses, and smooth-manifold structures. The hyperstructure paradigm extends these notions by allowing the operation to return subsets of [...] Read more.
Classical algebraic structures—such as magmas, groups, and Lie groups—are characterized by increasingly strong requirements in binary operation, ranging from no additional constraints to associativity, identity, inverses, and smooth-manifold structures. The hyperstructure paradigm extends these notions by allowing the operation to return subsets of elements, giving rise to hypermagmas, hypergroups, and Lie hypergroups, along with their variants such as quotient, reduced, and fuzzy hypergroups. In this work, we introduce the concept of superhyperstructures, obtained by iterating the powerset construction, and develop the theory of superhypermagmas and Lie superhypergroups. We further define and analyze quotient superhypergroups, reduced superhypergroups, and fuzzy superhypergroups, exploring their algebraic properties and interrelationships. Full article
(This article belongs to the Special Issue Feature Papers in Topology and Its Applications)
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