Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Einstein solvmanifolds attached to two-step nilradicals   A Riemannian Einstein solvmanifold (possibly, any noncompact homogeneous
Einstein space) is almost completely determined by the nilradical of its Lie
algebra. A nilpotent Lie algebra, which can serve as the nilradical of an
Einstein metric solvable Lie algebra, is called an Einstein nilradical. Despite
a substantial progress towards the understanding of Einstein nilradicals, there
is still a lack of classification results even for some well-studied classes of
nilpotent Lie algebras, such as the two-step ones. In this paper, we give a
classification of two-step nilpotent Einstein nilradicals in one of the rare
cases when the complete set of affine invariants is known: for the two-step
nilpotent Lie algebras with the two-dimensional center. Informally speaking, we
prove that such a Lie algebra is an Einstein nilradical, if it is defined by a
matrix pencil having no nilpotent blocks in the canonical form and no
elementary divisors of a very high multiplicity. We also discuss the connection
between the property of a two-step nilpotent Lie algebra and its dual to be an
Einstein nilradical.

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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: comp-gas