ON REGULAR SUBGROUPS OF THE AFFINE GROUP

DOI10.1017/S000497271400077XzbMath1314.20001OpenAlexW1977787225MaRDI QIDQ5175060

Paola Stefanelli, Ilaria Colazzo, Francesco Catino

Publication date: 19 February 2015

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s000497271400077x

zbMATH Keywords

Yang-Baxter equationaffine groupsradical ringsregular subgroupsbraces

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Jacobson radical, quasimultiplication (16N20) Characterization theorems for permutation groups (20B10)

Related Items (21)

Regular subgroups of the affine group and asymmetric product of radical braces. ⋮ Almost simple braces and primitive solutions to the Yang-Baxter equation ⋮ Set-theoretic solutions to the Yang-Baxter equation and generalized semi-braces ⋮ More on regular subgroups of the affine group ⋮ Uniconnected solutions to the Yang–Baxter equation arising from self-maps of groups ⋮ Semi-braces and the Yang-Baxter equation ⋮ The matched product of the solutions to the Yang-Baxter equation of finite order ⋮ Left non-degenerate set-theoretic solutions of the Yang–Baxter equation and dynamical extensions of q-cycle sets ⋮ The classification of nondegenerate uniconnected cycle sets ⋮ Module braces: relations between the additive and the multiplicative groups ⋮ Элементарные регулярные абелевы подгруппы аффинной группы векторного пространства в связи с анализом криптографических примитивов;Elementary Abelian regular subgroups of vector space affine group related to cryptanalysis ⋮ Primes in coverings of indecomposable involutive set-theoretic solutions to the Yang-Baxter equation ⋮ Skew left braces with non-trivial annihilator ⋮ On properties of translation groups in the affine general linear group with applications to cryptography ⋮ Iterated matched products of finite braces and simplicity; new solutions of the Yang-Baxter equation ⋮ Set-theoretic solutions of the Yang-Baxter equation and new classes of \(\mathrm{R}\)-matrices ⋮ L-algebras with duality and the structure group of a set-theoretic solution to the Yang-Baxter equation ⋮ Regular subgroups, nilpotent algebras and projectively congruent matrices ⋮ Classification of indecomposable involutive set-theoretic solutions to the Yang-Baxter equation ⋮ The matched product of set-theoretical solutions of the Yang-Baxter equation ⋮ Bijective 1-cocycles, braces, and non-commutative prime factorization

Cites Work

• Unnamed Item
• Braces, radical rings, and the quatum Yang-Baxter equation.
• Transitive subgroups of primitive permutation groups
• Dynamical braces and dynamical Yang-Baxter maps
• Regular subgroups of the affine group
• Braces and the Yang-Baxter equation
• Cohomology and representations of associative algebras
• Abelian Hopf Galois structures on prime-power Galois field extensions
• SEMIDIRECT PRODUCTS IN ALGEBRAIC LOGIC AND SOLUTIONS OF THE QUANTUM YANG–BAXTER EQUATION
• REGULAR SUBGROUPS OF THE AFFINE GROUP AND RADICAL CIRCLE ALGEBRAS

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