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Geometric classification of 4-dimensional superalgebras

Boekbijdrage - Boekhoofdstuk Conferentiebijdrage

In this paper, we give a geometric classification of 4-dimensional superalgebras over an algebraic closed field. It turns out that the number of irreducible components of the variety of 4-dimensional superalgebras Salg$_4$ under the Zariski topology is between 20 and 22. One of the significant differences between the variety Alg$_n$ and the variety Salg$_n$ is that Salg$_n$ is disconnected while Alg$_n$ is connected. Under certain conditions on $n$, one can show that the variety Salg$_n$ is the disjoint union of $n$ connected subvrieties. We shall present the degeneration diagrams of the 4 disjoint connected subvarieties Salg$^i_4$ of Salg$_4$.
Boek: Algebra, Geometry and Mathematical Physics: Proceedings of AGMP
Series: Springer Proceeding of Mathematics and Statistics
Pagina's: 291 - 323
ISBN:978-3-642-55360-8
Jaar van publicatie:2014
Toegankelijkheid:Closed