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Degenerations of pre-Lie algebras

J. Math. Phys. 50, 112102 (2009); doi:10.1063/1.3246608

Published 3 November 2009

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Thomas Beneš and Dietrich Burde
Fakultät für Mathematik, Universität Wien, Nordbergstr. 15, 1090 Wien, Austria
We consider the variety of pre-Lie algebra structures on a given n-dimensional vector space. The group GLn(K) acts on it, and we study the closure of the orbits with respect to the Zariski topology. This leads to the definition of pre-Lie algebra degenerations. We give fundamental results on such degenerations, including invariants and necessary degeneration criteria. We demonstrate the close relationship to Lie algebra degenerations. Finally, we classify all orbit closures in the variety of complex two-dimensional pre-Lie algebras. ©2009 American Institute of Physics
History: Received 17 April 2009; accepted 3 September 2009; published 3 November 2009
Permalink: http://link.aip.org/link/?JMAPAQ/50/112102/1
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ISSN:
0022-2488 (print)   1089-7658 (online)
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REFERENCES (13)
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