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SUMMARY:Norberto Gavioli (Università degli Studi dell'Aquila)
DTSTART:20210218T160000Z
DTEND:20210218T170000Z
DTSTAMP:20260423T021323Z
UID:GOThIC/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GOThIC/17/">
 Thin subalgebras of Lie algebras of maximal class</a>\nby Norberto Gavioli
  (Università degli Studi dell'Aquila) as part of GOThIC - Ischia Online G
 roup Theory Conference\n\n\nAbstract\nJoint work with M. Avitabile\, A. Ca
 ranti\, V. Monti\, M. F. Newman and E. O'Brien\n\nLet $L$ be an infinite d
 imensional Lie algebra which is graded over the positive integers and is g
 enerated by its first homogeneous component $L_1$. The algebra $L$ is of m
 aximal class if $\\dim(L_1)=2$ and $\\dim(L_i)=1$ for $1$ larger than $1$.
  The algebra $L$ is thin if it is not of maximal class\, $\\dim(L_1)=2$ an
 d $L_{i+1}=[x\,L_1]$ for any nontrivial element $x$ in $L_i$.\n\nSuppose t
 hat $E$ is a quadratic extension of a field $F$ and that $M$ is a Lie alge
 bra of maximal class over $E$. We consider the Lie algebra $L$ generated o
 ver the field $F$ by an $F$-subspace $L_1$ of $M_1$ having dimension $2$ o
 ver $F$. 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 constructe
 d by way of this “recipe”\, attaining the maximum possible cardinality
 .\n\nThe authors started this project almost independently since 1999 and 
 their partial results have been luckily and duly recorded by A. Caranti. O
 nly recently we have been able to develop together thorough and concise re
 sults for this research.\n
LOCATION:https://researchseminars.org/talk/GOThIC/17/
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