COHOMOLOGY AND EXTENSIONS OF BRACES

被引：28

作者：

Lebed, Victoria ^{[1
]}

Vendramin, Leandro ^{[2
]}

机构：

[1] Univ Nantes, Lab Math Jean Leray, 2 Rue Houssiniere,BP 92208, F-44322 Nantes 3, France

[2] Univ Buenos Aires, FCEN, Dept Matemat, Pabellon 1, RA-1428 Buenos Aires, DF, Argentina

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2016年 / 284卷 / 01期

关键词：

brace; cycle set; Yang-Baxter equation; extension; cohomology; YANG-BAXTER EQUATION; SET-THEORETIC SOLUTIONS; REGULAR SUBGROUPS; AFFINE GROUP; I-TYPE;

D O I：

10.2140/pjm.2016.284.191

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Braces and linear cycle sets are algebraic structures playing a major role in the classification of involutive set-theoretic solutions to the Yang-Baxter equation. This paper introduces two versions of their (co) homology theories. These theories mix the Harrison (co) homology for the abelian group structure and the (co) homology theory for general cycle sets, developed earlier by the authors. Different classes of brace extensions are completely classified in terms of second cohomology groups.

引用

页码：191 / 212

页数：22

共 27 条

[1]

Bachiller D., 2015, PREPRINT

[2] Classification of braces of order p3 [J].

Bachiller, David .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2015, 219 (08) :3568-3603

[3] On groups of I-type and involutive Yang-Baxter groups [J].

Ben David, Nir ;

Ginosar, Yuval .

JOURNAL OF ALGEBRA, 2016, 458 :197-206

[4] Regular subgroups of the affine group and asymmetric product of radical braces [J].

Catino, Francesco ;

Colazzo, Ilaria ;

Stefanelli, Paola .

JOURNAL OF ALGEBRA, 2016, 455 :164-182

[5] ON REGULAR SUBGROUPS OF THE AFFINE GROUP [J].

Catino, Francesco ;

Colazzo, Ilaria ;

Stefanelli, Paola .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2015, 91 (01) :76-85

[6] REGULAR SUBGROUPS OF THE AFFINE GROUP AND RADICAL CIRCLE ALGEBRAS [J].

Catino, Francesco ;

Rizzo, Roberto .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2009, 79 (01) :103-107

[7] Braces and the Yang-Baxter Equation [J].

Cedo, Ferran ;

Jespers, Eric ;

Okninski, Jan .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2014, 327 (01) :101-116

[8] Retractability of set theoretic solutions of the Yang-Baxter equation [J].

Cedo, Ferran ;

Jespers, Eric ;

Okninski, Jan .

ADVANCES IN MATHEMATICS, 2010, 224 (06) :2472-2484

[9]

Cedó F, 2010, T AM MATH SOC, V362, P2541

[10] GARSIDE GROUPS AND YANG-BAXTER EQUATION [J].

Chouraqui, Fabienne .

COMMUNICATIONS IN ALGEBRA, 2010, 38 (12) :4441-4460

← 1 2 3 →