1Faculty of Mathematics and Computer Science, University of Warmia and Mazury, ul. Sloneczna 54, 10-710 Olsztyn, Poland 2Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NASU, Naukova St. 3-b, 79060 L'viv, Ukraine
Journal of Lie Theory, Tome 24 (2014) no. 2, pp. 561-623
We propose an approach to a long-standing problem of classification of pairs of compatible Lie-algebra structures, one of which is semisimple. Any such pair is determined by a linear operator which is defined up to the addition of a derivation. We introduce a special fixing of this operator to get rid of this ambiguity and consider the operators preserving the root decomposition with respect to a Cartan subalgebra. The classification leads to two disjoint classes of pairs depending on the symmetry properties of the corresponding operator with respect to the Killing form. We present a list of known and new examples in each case and conjecture the completeness of these lists.
1
Faculty of Mathematics and Computer Science, University of Warmia and Mazury, ul. Sloneczna 54, 10-710 Olsztyn, Poland
2
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NASU, Naukova St. 3-b, 79060 L'viv, Ukraine
Andriy Panasyuk. Compatible Lie Brackets: Towards a Classification. Journal of Lie Theory, Tome 24 (2014) no. 2, pp. 561-623. http://geodesic.mathdoc.fr/item/JOLT_2014_24_2_a12/
@article{JOLT_2014_24_2_a12,
author = {Andriy Panasyuk},
title = {Compatible {Lie} {Brackets:} {Towards} a {Classification}},
journal = {Journal of Lie Theory},
pages = {561--623},
year = {2014},
volume = {24},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2014_24_2_a12/}
}
TY - JOUR
AU - Andriy Panasyuk
TI - Compatible Lie Brackets: Towards a Classification
JO - Journal of Lie Theory
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