caa a22 4500 445884606 CHVBK 20180317145555.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s10711-010-9546-z doi (NATIONALLICENCE)springer-10.1007/s10711-010-9546-z Jablonski Michael Department of Mathematics, University of Oklahoma, 73019-0315, Norman, OK, USA aut Moduli of Einstein and non-Einstein nilradicals [Elektronische Daten] [Michael Jablonski] A nilpotent Lie algebra is called an Einstein nilradical if the corresponding Lie group admits a left-invariant Ricci soliton metric. While these metrics are of independent interest, their existence is intimately related to the existence of Einstein metrics on solvable Lie groups. In this note we are concerned with the following question: How are the Einstein and non-Einstein nilradicals distributed among nilpotent Lie algebras? A full answer to this question is not known and we restrict to the class of 2-step nilpotent Lie groups. Within this class, it is known that a generic group admits a Ricci soliton metric. Using techniques from Geometric Invariant Theory, we study the set of non-generic algebras to learn more about the distribution of non-Einstein nilradicals. Many new (continuous) families of non-isomorphic, non-Einstein nilradicals are constructed. Moreover, the dimension of these families can be arbitrarily large (depending on the dimension of the underlying Lie group). To show such large classes of Lie groups are pairwise non-isomorphic, a new technique is developed to distinguish between Lie algebras. Springer Science+Business Media B.V., 2010 Nilpotent Lie group nationallicence Einstein nilradical nationallicence Ricci soliton nationallicence Distinguished orbit nationallicence Geometriae Dedicata Springer Netherlands 152/1(2011-06-01), 63-84 0046-5755 152:1<63 2011 152 10711 https://doi.org/10.1007/s10711-010-9546-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9546-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Jablonski Michael Department of Mathematics, University of Oklahoma, 73019-0315, Norman, OK, USA aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 152/1(2011-06-01), 63-84 0046-5755 152:1<63 2011 152 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer