Skew braces: a brief survey. (English) Zbl 07919707
Kielanowski, Piotr (ed.) et al., Geometric methods in physics XL, workshop, Białowieża, Poland, June 20–25, 2023. Cham: Birkhäuser. Trends Math., 153-175 (2024).
Found 138 Documents (Results 1–100)
Skew braces and the braid equation on sets. (English) Zbl 07919706
Kielanowski, Piotr (ed.) et al., Geometric methods in physics XL, workshop, Białowieża, Poland, June 20–25, 2023. Cham: Birkhäuser. Trends Math., 145-152 (2024).
Twisted Araki-Woods algebras, the Yang-Baxter equation, and quantum field theory. (English) Zbl 07919705
Kielanowski, Piotr (ed.) et al., Geometric methods in physics XL, workshop, Białowieża, Poland, June 20–25, 2023. Cham: Birkhäuser. Trends Math., 127-144 (2024).
Skew left braces and the Yang-Baxter equation. (English) Zbl 07865149
Reviewer: Leandro Vendramin (Brussel)
More on skew braces and their ideals. (English) Zbl 07861181
Mann, Avinoam (ed.) et al., Amitsur centennial symposium, virtual and the Israel Institute for Advanced Studies (IIAS), The Hebrew University of Jerusalem, Jerusalem, Israel, November 1–4, 2021. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 800, 301-308 (2024).
Involutive Yang-Baxter: cabling, decomposability, and Dehornoy class. (English) Zbl 07835934
Reviewer: Agata Pilitowska (Warszawa)
Dehornoy’s class and Sylows for set-theoretical solutions of the Yang-Baxter equation. (English) Zbl 07817039
Reviewer: Leandro Vendramin (Brussel)
From braces to pre-Lie rings. (English) Zbl 1537.17052
Reviewer: Cindy Tsang (Tōkyō)
Post-groups, (Lie-)Butcher groups and the Yang-Baxter equation. (English) Zbl 1535.22061
Reviewer: Lorenzo Stefanello (Pisa)
Schur covers of skew braces. (English) Zbl 07804819
Set-theoretic type solutions of the braid equation. (English) Zbl 1539.16024
Reviewer: Marzia Mazzotta (Lecce)
Near braces and \(p\)-deformed braided groups. (English) Zbl 07798501
Reviewer: Paola Stefanelli (Lecce)
Skew left braces and 2-reductive solutions of the Yang-Baxter equation. (English) Zbl 07784724
Reviewer: Leandro Vendramin (Brussel)
Cohomology, extensions and automorphisms of skew braces. (English) Zbl 1529.20048
Reviewer: Christopher P. Bendel (Menomonie)
Central endomorphisms of groups and radical rings. (English) Zbl 1536.20043
Reviewer: Enrico Jabara (Venezia)
Modules over trusses vs. modules over rings: internal direct sums. (English) Zbl 1530.16049
Chabert, Jean-Luc (ed.) et al., Algebraic, number theoretic, and topological aspects of ring theory. Selected papers based on the cancelled conference on rings and polynomials, July 2020, and the fourth international meeting on integer-valued polynomials and related topics, CIRM, Luminy, France, July 19–24, 2021. Cham: Springer. 171-185 (2023).
A characterization of finite simple set-theoretic solutions of the Yang-Baxter equation. (English) Zbl 1536.16032
Reviewer: Oleksandr Tsymbaliuk (West Lafayette)
Operated groups, differential groups and Rota-Baxter groups with an emphasis on the free objects. (English) Zbl 1530.20100
Reviewer: Egle Bettio (Venezia)
Module braces: relations between the additive and the multiplicative groups. (English) Zbl 1532.16029
Reviewer: Cindy Tsang (Tōkyō)
Indecomposable solutions of the Yang-Baxter equation of square-free cardinality. (English) Zbl 1531.16029
Reviewer: Marzia Mazzotta (Lecce)
Nilpotency of skew braces and multipermutation solutions of the Yang-Baxter equation. (English) Zbl 1533.16063
Reviewer: Ramón González Rodríguez (Vigo)
Indecomposable solutions of the Yang-Baxter equation with permutation group of sizes \(pq\) and \(p^2 q\). (English) Zbl 1528.16033
Reviewer: Lorenzo Stefanello (Pisa)
Set-theoretical solutions to the Hom-Yang-Baxter equation and Hom-cycle sets. (English) Zbl 1527.16035
Reviewer: Marzia Mazzotta (Lecce)
From braces to Hecke algebras and quantum groups. (English) Zbl 1533.16059
Reviewer: Marzia Mazzotta (Lecce)
On some Garsideness properties of structure groups of set-theoretic solutions of the Yang-Baxter equation. (English) Zbl 1517.20065
Reviewer: Enrico Jabara (Venezia)
The Yang-Baxter equation and Thompson’s group \(F\). (English) Zbl 1522.20227
Reviewer: Huafeng Zhang (Villeneuve d’Ascq)
Indecomposable involutive solutions of the Yang-Baxter equation of multipermutation level 2 with non-abelian permutation group. (English) Zbl 1525.16032
Reviewer: Nenad Manojlović (Faro)
Extensions of linear cycle sets and cohomology. (English) Zbl 1517.20045
Reviewer: Lorenzo Stefanello (Pisa)
Rota-Baxter systems and skew trusses. (English) Zbl 1514.17019
Reviewer: Cindy Tsang (Tokyo)
Rota-Baxter operators on Clifford semigroups and the Yang-Baxter equation. (English) Zbl 1517.17015
Reviewer: Hirokazu Nishimura (Tsukuba)
Skew braces from Rota-Baxter operators: a cohomological characterisation and some examples. (English) Zbl 1508.17023
On various types of nilpotency of the structure monoid and group of a set-theoretic solution of the Yang-Baxter equation. (English) Zbl 1510.16031
Reviewer: Thomas Weber (Torino)
Braces whose additive group has a cyclic maximal subgroup. (English) Zbl 1515.81159
Front. Math. China 17, No. 6, 1051-1061 (2022); translation from Adv. Math., Beijing 50, No. 6, 907-916 (2021).
The fundamental theorem of Hopf modules for Hopf braces. (English) Zbl 1504.18015
Reviewer: J. N. Alonso Alvarez (Vigo)
The construction of braided tensor categories from Hopf braces. (English) Zbl 1510.16030
Reviewer: Loïc Foissy (Calais)
Primitive set-theoretic solutions of the Yang-Baxter equation. (English) Zbl 1512.16031
Reviewer: Paola Stefanelli (Lecce)
On the passage from finite braces to pre-Lie rings. (English) Zbl 1512.17055
Reviewer: Cindy Tsang (Tokyo)
Classification of non-degenerate involutive set-theoretic solutions to the Yang-Baxter equation with multipermutation level two. (English) Zbl 1513.81087
Brace blocks from bilinear maps and liftings of endomorphisms. (English) Zbl 1512.20004
Reviewer: Peter Danchev (Sofia)
Left non-degenerate set-theoretic solutions of the Yang-Baxter equation and semitrusses. (English) Zbl 1511.16030
Reviewer: J. N. Alonso Alvarez (Vigo)
Bijective 1-cocycles, braces, and non-commutative prime factorization. (English) Zbl 1508.16043
Reviewer: Paola Stefanelli (Lecce)
Quasi-bialgebras from set-theoretic type solutions of the Yang-Baxter equation. (English) Zbl 1517.16028
Reviewer: Marzia Mazzotta (Lecce)
Left non-degenerate set-theoretic solutions of the Yang-Baxter equation and dynamical extensions of \(q\)-cycle sets. (English) Zbl 1507.16038
Reviewer: Leandro Vendramin (Buenos Aires)
Cocyclic braces and indecomposable cocyclic solutions of the Yang-Baxter equation. (English) Zbl 1514.16030
Reviewer: Marzia Mazzotta (Lecce)
Nilpotency in left semi-braces. (English) Zbl 1498.16042
Reviewer: Marzia Mazzotta (Lecce)
The Baer-Kaplansky theorem for all abelian groups and modules. (English) Zbl 1511.20207
Reviewer: Grigore Călugăreanu (Cluj-Napoca)
Ideal ring extensions and trusses. (English) Zbl 1502.16029
Reviewer: Stefan Veldsman (Port Elizabeth)
New simple solutions of the Yang-Baxter equation and solutions associated to simple left braces. (English) Zbl 1495.16031
Reviewer: Marzia Mazzotta (Lecce)
Some braces of cardinality \(p^4\) and related Hopf-Galois extensions. (English) Zbl 1495.16032
Reviewer: Cindy Tsang (Tokyo)
Algebraic approach to Rump’s results on relations between braces and pre-Lie algebras. (English) Zbl 1505.16048
Reviewer: J. N. Alonso Alvarez (Vigo)
Radford’s theorem about Hopf braces. (English) Zbl 1505.16047
Reviewer: Loïc Foissy (Calais)
Rota-Baxter groups, skew left braces, and the Yang-Baxter equation. (English) Zbl 1492.17019
Reviewer: Cindy Tsang (Tokyo)
On \(\mathbb{Z}_n \rtimes \mathbb{Z}_2\)-Hopf-Galois structures. (English) Zbl 1485.12006
Reviewer: Cindy Tsang (Tokyo)
A new formula for Lazard’s correspondence for finite braces and pre-Lie algebras. (English) Zbl 1505.16066
Reviewer: Teresa Crespo (Barcelona)
Braces whose additive group has a cyclic maximal subgroup. (Chinese. English summary) Zbl 1513.81086
Set-theoretic solutions to the Yang-Baxter equation and generalized semi-braces. (English) Zbl 1500.16036
Reviewer: J. N. Alonso Alvarez (Vigo)
Indecomposable involutive solutions of the Yang-Baxter equation of multipermutational level 2 with abelian permutation group. (English) Zbl 1494.16036
Indecomposable involutive set-theoretic solutions of the Yang-Baxter equation and orthogonal dynamical extensions of cycle sets. (English) Zbl 1490.16081
Reviewer: Agata Pilitowska (Warszawa)
Constructing finite simple solutions of the Yang-Baxter equation. (English) Zbl 1485.16032
Adv. Math. 391, Article ID 107968, 40 p. (2021); corrigendum ibid. 451, Article ID 109807, 3 p. (2024).
Reviewer: Cristian Vay (Córdoba)
Structure monoids of set-theoretic solutions of the Yang-Baxter equation. (English) Zbl 1487.16035
Publ. Mat., Barc. 65, No. 2, 499-528 (2021); corrigendum and addendum ibid. 68, No. 1, 241-250 (2024).
Reviewer: Ilaria Colazzo (Exeter)
Set-theoretic Yang-Baxter & reflection equations and quantum group symmetries. (English) Zbl 1486.16039
Reviewer: Matthew Harper (Columbus)
The structure group and the permutation group of a set-theoretic solution of the quantum Yang-Baxter equation. (English) Zbl 1475.16036
Two theorems on balanced braces. (English) Zbl 1482.16060
Reviewer: J. N. Alonso Alvarez (Vigo)
Congruence classes and extensions of rings with an application to braces. (English) Zbl 1467.16048
Reviewer: Leandro Vendramin (Buenos Aires)
On skew braces and their ideals. (English) Zbl 1476.16036
Exp. Math. 30, No. 1, 95-104 (2021); erratum ibid. 31, No. 1, 346 (2022).
Reviewer: J. N. Alonso Alvarez (Vigo)
MSC:
16T25
Inverse semi-braces and the Yang-Baxter equation. (English) Zbl 1476.16035
Reviewer: Kenny De Commer (Brussels)
Set-theoretic solutions of the Yang-Baxter equation, associated quadratic algebras and the minimality condition. (English) Zbl 1466.16034
Reviewer: Cristian Vay (Córdoba)
Involutive Latin solutions of the Yang-Baxter equation. (English) Zbl 1460.16036
Reviewer: J. N. Alonso Alvarez (Vigo)
The algebraic structure of left semi-trusses. (English) Zbl 1461.16038
Reviewer: Stefan Veldsman (Port Elizabeth)
Every finite abelian group is a subgroup of the additive group of a finite simple left brace. (English) Zbl 1461.16037
Reviewer: Agata Pilitowska (Warszawa)
An abundance of simple left braces with abelian multiplicative Sylow subgroups. (English) Zbl 1466.16035
Reviewer: Leandro Vendramin (Buenos Aires)
Set-theoretic solutions of the pentagon equation. (English) Zbl 1482.16059
Reviewer: Agata Pilitowska (Warszawa)
An associative left brace is a ring. (English) Zbl 1467.16037
Reviewer: Agata Pilitowska (Warszawa)
Set-theoretical solutions of the Yang-Baxter and pentagon equations on semigroups. (English) Zbl 1508.20081
About a question of Gateva-Ivanova and Cameron on square-free set-theoretic solutions of the Yang-Baxter equation. (English) Zbl 1461.16036
Reviewer: Marzia Mazzotta (Lecce)
MSC:
16T25
The matched product of the solutions to the Yang-Baxter equation of finite order. (English) Zbl 1439.16035
Affine structures of decomposable solvable groups. (English) Zbl 1473.17090
Reviewer: Cindy Tsang (Tokyo)
On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size. (English) Zbl 1481.16043
Reviewer: Daniel Bulacu (Bucharest)
Skew braces of size \(pq\). (English) Zbl 1437.16027
Reviewer: Wolfgang Rump (Stuttgart)
MSC:
16T25
Distributive biracks and solutions of the Yang-Baxter equation. (English) Zbl 1464.16030
Reviewer: Marzia Mazzotta (Lecce)
Retractability of solutions to the Yang-Baxter equation and \(p\)-nilpotency of skew braces. (English) Zbl 1436.16044
Reviewer: Wolfgang Rump (Stuttgart)
MSC:
16T25
Combinatorial solutions to the reflection equation. (English) Zbl 1444.16050
Reviewer: Eric Jespers (Brüssel)
MSC:
16T25
The matched product of set-theoretical solutions of the Yang-Baxter equation. (English) Zbl 1435.16008
Reviewer: Andrea Caranti (Trento)
Asymmetric product of left braces and simplicity; new solutions of the Yang-Baxter equation. (English) Zbl 1451.16029
Reviewer: Victoria Lebed (Caen)
Factorizations of skew braces. (English) Zbl 1446.16040
Reviewer: Daniel Simson (Toruń)
The structure monoid and algebra of a non-degenerate set-theoretic solution of the Yang-Baxter equation. (English) Zbl 1432.16032
Trans. Am. Math. Soc. 372, No. 10, 7191-7223 (2019); corrigendum ibid. 373, No. 6, 4517-4521 (2020).
Reviewer: Sorin Dascalescu (Bucureşti)
Actions of skew braces and set-theoretic solutions of the reflection equation. (English) Zbl 1470.16068
Dynamical extensions of quasi-linear left cycle sets and the Yang-Baxter Equation. (English) Zbl 1422.16035
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