Results 91 to 100 of about 2,017 (174)
An Application of Co-Medial Algebras with Quasigroup Operations on Cryptology
, 2014 A modification of Markovski quasigroup based crypto-algorytm has been presented. This modification is based on the pair of co-medial quasigroup operations, which we show that they are orthogonal quasigroup operations.
A. Ehsani
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Quasigroups and related systems, 2011 In this paper the concept of pentagonal quasigroup is introduced as {; ; ; IM}; ; ; -quasigroup satisfying the additional property of pentagonality. Some basic identities which are valid in a general pentagonal quasigroup are proved. Four different models for pentagonal quasigroups and their mutual relations are studied.
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, 2015 Parastrophes (conjugates) of a quasigroup can be divided into separate classes containing isotopic parastrophes. We prove that the number of such classes is always 1, 2, 3 or 6. Next we characterize quasigroups having a fixed number of such classes.
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The Universality of the variety of quasigroups [PDF]
Journal of the Australian Mathematical Society, 1976 AbstractThe variety of quasigroups is universal for varieties of algebras of the most general kind in the sense that each such variety can be interpreted in a natural way in a suitably chosen subvariety of quasigroups. More precisely, for any algebra〈A, f0, f1, f2, …〉wheref0, f1, f2, …is an arbitrary finite or infinite sequence of operations of finite ...
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The Burnside algebra of a quasigroup
Journal of Algebra, 2004 In this paper the author extends the Burnside algebra concept from groups to quasigroups. Given a subquasigroup \(P\) of a finite quasigroup \(Q\), the elements of the corresponding homogeneous space \(P\setminus Q\) are the orbits on \(Q\) of the relative left multiplication group of \(P\) in \(Q\).
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Asian Journal of Mathematics, 2016 In this paper we introduce the notion of weak Hopf quasigroup as a generalization of weak Hopf algebras and Hopf quasigroups. We obtain its main properties and we prove the fundamental theorem of Hopf modules for these algebraic structures.
Álvarez, J. N. Alonso +2 more
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Representation of a gauge field via intrinsic “BRST” operator
Physics Letters B, 2015 We show that there exists a representation of a matrix-valued gauge field via intrinsic “BRST” operator assigned to matrix-valued generators of a gauge algebra. In this way, we reproduce the standard formulation of the ordinary Yang–Mills theory.
Igor A. Batalin, Peter M. Lavrov
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Quasigroups, right quasigroups, coverings and representations
, 2018 For a fixed quasigroup Q, equivalences are established between the following categories: (i) the category of modules over the quasigroup; (ii) the category of representations of a stabilizer in the universal multiplication group; (iii) the category of representations of the fundamental groupoid of the Cayley diagram of the quasigroup in the category of
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Note on Quasigroups and Trees [PDF]
Proceedings of the Edinburgh Mathematical Society, 1963 If letters a, b, c, … are used to denote points of a nondegenerate plane cubic curve, other than the singular point if any, and if the product ab is defined as the third point of the curve collinear with a and b, we obtain an algebraic system having nonassociative multiplication (ab . c ≠ a . bc in general).
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Journal of Algebra, 2016 A quantum quasigroup is a family \((A,\nabla,\Delta)\), where \((A,\nabla)\) is a magma in a given symmetric monoidal category, \((A,\Delta)\) is a comagma in the same category, such that the compositions \((\Delta\otimes 1_A)\circ(1_A\otimes\nabla)\) and \((1_A\otimes\Delta)(\nabla\otimes 1_A)\) are invertible.
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