Talk «Triply factorised groups and skew left braces» at Ischia Online Group Theory Conference (GOThIC) on 19th November, 2020

Nov ’20

The organising committee of the
Ischia Online Group Theory Conference(GOThIC)
is inviting you to a scheduled Zoom meeting.


– The TIME OF THE TALK is 17:00 CET = UTC + 1.

– You are welcome to share the Zoom link with other interested

– When joining, please MAKE SURE THAT YOUR NICKNAME
IS YOUR NAME AND SURNAME, or close to it, so that the organisers
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The Ischia Group Theory 2020 Conference
( was planned
for 30 March – 4 April 2020. It has now been postponed.
In the meantime, we are offering a series of online lectures
by leading researchers (

TIME: November 19th, 2020 17:00 CET (UTC+1)

COFFEE BREAK: The talk will start at 17:00 CET. The conference room
will open at 16:45 CET for a coffee break
– Bring Your Own tea/coffee mug – biscuits appreciated –
and join us for some smalltalk before the event.

SPEAKER: Ramon Esteban-Romero (Universitat de València)

TITLE: Triply factorised groups and skew left braces


The Yang-Baxter equation is a consistency equation of the statistical mechanics proposed by Yang [6] and Baxter [1] that describes the interaction of many particles in some scattering situations. This equation lays the foundation for the theory of quantum groups and Hopf algebras. During the last years, the study suggested by Drinfeld [2] of the so-called set-theoretic solutions of the Yang-Baxter equation has motivated the appearance of many algebraic structures. Among these structures we find the skew left braces, in troduced by Guarnieri and Vendramin [3] as a generalisation of the structure of left brace defined by Rump [4]. It consists of a set B with two operations + and ·, not necessarily commutative, that give B two structures of group linked by a modified distributive law.

The multiplicative group C = (B, ·) of a skew left brace (B, +, ·) acts on the multiplicative group K = (B, +) by means of an action λ: C −→ Aut(K) given by λ(a)(b) = −a + a · b, for a, b ∈ B. With respect to this action, the identity map δ : C −→ K becomes a derivation or 1-cocycle with respect to λ. In the semidirect product G = [K]C = {(k, c) | k ∈ K, c ∈ C}, there is a diagonal-type subgroup D = {(δ(c), c) | c ∈ C} such that G = KD = CD, K ∩ D = C ∩ D = 1. This approach was presented by Sysak in [5] and motivates the use of techniques of group theory to study skew left braces.

We present in this talk some applications of this approach to obtain some results about skew left braces. These results have been obtained in collaboration with Adolfo Ballester-Bolinches.

Recorded talks: