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# Seminario Gavioli

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

PLEASE NOTE:

- The TIME OF THE TALK is 19:00 CET (CET = UTC + 1). ******NOTE THE UNUSUAL TIME!******

- You  are  welcome to  share  the  Zoom  link with  other  interested
parties, but PLEASE DO NOT POST THE LINK PUBLICLY.

- When joining, please  MAKE SURE THAT YOUR NICKNAME IS  YOUR NAME AND
SURNAME, or  close to it, so  that the organisers can  recognise you
and let you in

The Ischia Group Theory 2020 Conference
(http://www.dipmat2.unisa.it/ischiagrouptheory/), planned for
30 March - 4 April 2020, was postponed. In the
meantime, we are organising a series of online lectures by leading
researchers (https://sites.google.com/unisa.it/e-igt2020/).

TIME: Thursday February 18th, 2021 19:00 CET (UTC+1) *****NOTE THE UNUSUAL TIME!*******
COFFEE BREAK: The  talk will start at 19:00 CET.
The conference room will open at 18:45 CET for a drink
- Bring Your Own appropriate drink - biscuits appreciated -
and join us for some smalltalk before the event.
SPEAKER: Norberto Gavioli (University of L’Aquila)

Title:Thin subalgebras of Lie algebras of maximal class

Abstract:  (Joint work with M. Avitabile, A. Caranti, V. Monti, M. F. Newman and E. OBrien).
Let L be an infinite
dimensional Lie algebra which is graded over the positive integers and is generated by its first homogeneous component L_1. The algebra L is of maximal class if dim(L_1)=2 and dim(L_i)=1 for i larger than 1. The algebra L is thin if it is not of maximal class, dim(L_1)=2 and L_{i+1}=[x,L_1] for any nontrivial element x in L_i.

Suppose that E is a quadratic extension of a field F and that M is a Lie algebra of maximal class over E. We consider the Lie algebra L generated over the field F by an F-subspace L_1 of M_1 having dimension 2 over F. We give necessary and sufficient conditions for the Lie algebra L to be a thin graded F-subalgebra of the F-algebra M. We show also that there are uncountably many such thin algebras that can be constructed by way of this “recipe”, attaining the maximum possible cardinality.

The authors started this project almost independently since 1999 and their partial results have been luckily and duly recorded by A. Caranti. Only recently we have been able to jointly develop thorough and concise results for this research.

16 febbraio 2021
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