The brace of a classical group

By Wolfgang Rump. 2014

80 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/af2bad5831d5017da9739389cae24d7d922ca363

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

Skew left braces of nilpotent type (2018, background): “New connections appeared, for example with regular subgroups and Hopf–Galois extensions [2], left orderable groups [5], flat manifolds [25].”
Factorizations of skew braces (2019, background): “e right algebraic framework to study set-theoretic solutions of the Yang{Baxter equation [16,23]. Skew braces are intensively studied, as they are known to have connections to several dierent topics [2,8,11,24,26]. The structure group and the permutation group of a solution are examples of skew brac”
Problems on skew left braces (2018, background): “The author thanks F. Cedó, T. Gateva–Ivanova, E. Jespers, V. Lebed, K. Nejabati Zenouz, J. Okniński, A. Smoktunowicz, W. Rump, P. Zadunaisky for discussions, comments and problems.”
Iterated matched products of finite braces and simplicity; new solutions of the Yang-Baxter equation (2016, background): “Rump initiated the study of this new algebraic structure, though, using another but equivalent definition [30, 31, 32, 33, 34, 35, 36].”
On skew braces (with an appendix by N. Byott and L. Vendramin) (2017, background): “In [44], Rump introduced braces, a new algebraic structure that turns out to be equivalent to bijective 1-cocycles; see [13, 27, 47].”
Post-groups, (Lie-)Butcher groups and the Yang–Baxter equation (2023, methodology): “A simple algebraic formula for the correspondence between finite right nilpotent Fp-braces and finite nilpotent pre-Lie algebras over the field Fp is obtained by Smoktunowicz [51], which agrees with the correspondence using Lazard’s correspondence between finite Fp-braces and pre-Lie algebras propos”
Counterexample to a conjecture about braces (2015, methodology): “2 Our first attempt was to use Lp for p = 11, as is suggested in [19], and repeat the computer calculations of [4].”