REGULAR SUBGROUPS OF THE AFFINE GROUP AND RADICAL CIRCLE ALGEBRAS

By F. Catino, Roberto Rizzo. Bulletin of the Australian Mathematical Society, 2009

54 citations recorded by the source corpus.

Abstract We establish a link between regular subgroups of the affine group and radical circle algebras on the underlying vector space.

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Extensions, matched products, and simple braces (2015, methodology): “Besides its relation with theoretical physics, this class of solutions is important for its connections with many branches of algebra, for instance: semigroups of I-type and Bieberbach groups [12], bijective 1-cocycles [10], radical rings [17], triply factorized groups [19], construction of semisimp”
Problems on skew left braces (2018, methodology): “Those braces were introduced by Catino and Rizzo in [20] as circle algebras.”
Iterated matched products of finite braces and simplicity; new solutions of the Yang-Baxter equation (2016, background): “In this section, we ﬁrst present a family of left braces with trivial socle, that generalizes the family presented by Heged˝us [24] and Catino and Rizzo in [10].”
Braces and the Yang–Baxter Equation (2012, methodology): “A connection of this type in the context of regular permutation subgroups of the affine group AGL(V ) on a vector space V was given by Catino and Rizzo [5].”
Solutions of the Yang-Baxter equation associated with a left brace (2015, background): “the Yang-Baxter equation in physics, but also for its connection with other topics in mathematics of recent interest: semigroups of I-type and Bieberbach groups [16], bijective 1-cocycles [11], radical rings [23], triply factorized groups [25], construction of semisimple minimal triangular Hopf alge”