scholarly journals Ternary and n-ary f-distributive structures

2018 ◽  
Vol 16 (1) ◽  
pp. 32-45 ◽  
Author(s):  
Indu R. U. Churchill ◽  
M. Elhamdadi ◽  
M. Green ◽  
A. Makhlouf
Keyword(s):  
Cohomology Theory ◽  
Extension Theory ◽  
Low Dimensions

AbstractWe introduce and study ternary f-distributive structures, Ternary f-quandles and more generally their higher n-ary analogues. A classification of ternary f-quandles is provided in low dimensions. Moreover, we study extension theory and introduce a cohomology theory for ternary, and more generally n-ary, f-quandles. Furthermore, we give some computational examples.

Classification of Filiform Leibniz Algebras in Low Dimensions

2019 ◽  
pp. 223-249
Author(s):  
Shavkat Ayupov ◽  
Bakhrom Omirov ◽  
Isamiddin Rakhimov
Keyword(s):  
Low Dimensions ◽  
Leibniz Algebras

NULL HELICES IN LORENTZIAN SPACE FORMS

2001 ◽  
Vol 16 (30) ◽  
pp. 4845-4863 ◽  
Author(s):  
ANGEL FERRÁNDEZ ◽  
ANGEL GIMÉNEZ ◽  
PASCUAL LUCAS
Keyword(s):  
Minkowski Space ◽  
Complete Classification ◽  
Space Forms ◽  
Lorentzian Space ◽  
Low Dimensions ◽  
Minkowski Space Time ◽  
Minimum Number ◽  
Null Curves ◽  
Lorentzian Space Forms

In this paper we introduce a reference along a null curve in an n-dimensional Lorentzian space with the minimum number of curvatures. That reference generalizes the reference of Bonnor for null curves in Minkowski space–time and it is called the Cartan frame of the curve. The associated curvature functions are called the Cartan curvatures of the curve. We characterize the null helices (that is, null curves with constant Cartan curvatures) in n-dimensional Lorentzian space forms and we obtain a complete classification of them in low dimensions.

scholarly journals COHOMOLOGY OF FROBENIUS ALGEBRAS AND THE YANG-BAXTER EQUATION

2008 ◽  
Vol 10 (supp01) ◽  
pp. 791-814 ◽  
Author(s):  
J. SCOTT CARTER ◽  
ALISSA S. CRANS ◽  
MOHAMED ELHAMDADI ◽  
ENVER KARADAYI ◽  
MASAHICO SAITO
Keyword(s):  
Deformation Theory ◽  
Hochschild Cohomology ◽  
Cohomology Theory ◽  
Baxter Equation ◽  
Low Dimensions ◽  
Frobenius Algebras

A cohomology theory for multiplications and comultiplications of Frobenius algebras is developed in low dimensions, in analogy with Hochschild cohomology of bialgebras, based on deformation theory. Concrete computations are provided for key examples. Skein theoretic constructions give rise to solutions to the Yang-Baxter equation, using multiplications and comultiplications of Frobenius algebras, and 2-cocycles are used to obtain deformations of R-matrices thus obtained.

The classification of Novikov algebras in low dimensions

2001 ◽  
Vol 34 (8) ◽  
pp. 1581-1594 ◽  
Author(s):  
Chengming Bai ◽  
Daoji Meng
Keyword(s):  
Low Dimensions ◽  
Novikov Algebras

Stable mappings of discriminant varieties

1988 ◽  
Vol 103 (1) ◽  
pp. 69-82
Author(s):  
J. W. Bruce
Keyword(s):  
Wave Front ◽  
Smooth Surfaces ◽  
Isolated Singularity ◽  
Isolated Singularities ◽  
Low Dimensions

Smooth mappings defined on discriminant varieties of -versal unfoldings of isolated singularities arise in many interesting geometrical contexts, for example when classifying outlines of smooth surfaces in ℝ3 and their duals, or wave-front evolution [1, 2, 5]. In three previous papers we have classified various stable mappings on discriminants. When the isolated singularity is weighted homogeneous the discriminant is not a local smooth product, and this makes the classification of stable germs considerably easier than in general. Moreover, discriminants arising from weighted homogeneous singularities predominate in low dimensions, so such classifications are very useful for applications.

scholarly journals The Magic of Universal Quantum Computing with Permutations

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Michel Planat ◽  
Rukhsan Ul Haq
Keyword(s):  
Quantum Computing ◽  
Wigner Function ◽  
Low Dimensions ◽  
State Dependent ◽  
Universal Quantum ◽  
Discrete Wigner Function

The role of permutation gates for universal quantum computing is investigated. The “magic” of computation is clarified in the permutation gates, their eigenstates, the Wootters discrete Wigner function, and state-dependent contextuality (following many contributions on this subject). A first classification of a few types of resulting magic states in low dimensions d≤9 is performed.

scholarly journals f-Racks, f-quandles, their extensions and cohomology

2017 ◽  
Vol 16 (11) ◽  
pp. 1750215 ◽  
Author(s):  
Indu R. U. Churchill ◽  
Mohamed Elhamdadi ◽  
Matthew Green ◽  
Abdenacer Makhlouf
Keyword(s):  
Cohomology Theory ◽  
Low Order

The purpose of this paper is to introduce and study the notions of [Formula: see text]-rack and [Formula: see text]-quandle which are obtained by twisting the usual equational identities by a map. We provide some key constructions, examples and classification of low order [Formula: see text]-quandles. Moreover, we define modules over [Formula: see text]-racks, discuss extensions and define a cohomology theory for [Formula: see text]-quandles and give examples.

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