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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/17234

Title: Geometric classification of 4-dimensional superalgebras
Authors: Armour, Aaron
Zhang, Yinhuo
Issue Date: 2014
Publisher: Springer
Citation: Makhlouf, A.; Paal, E.; Silvestrov, S.; Stolin, A. (Ed.). Algebra, Geometry and Mathematical Physics: Proceedings of AGMP, p. 291-323
Series/Report: Springer Proceeding of Mathematics and Statistics
Abstract: 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$_4$.
URI: http://hdl.handle.net/1942/17234
DOI: 10.1007/978-3-642-55361-5
ISBN: 978-3-642-55360-8
ISSN: 2194-1009
Category: C1
Type: Proceedings Paper
Appears in Collections: Research publications

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