Double extensions on Riemannian Ricci nilsolitons
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题目：Double extensions on Riemannian Ricci nilsolitons
摘要：A metric Lie algebra (\mathfrak g,< , >) is a Lie algebra \mathfrak g equipped with an indefinite inner product < , >. It naturally corresponds to a connected and simply connected Lie group manifold (G,g) with Lie algebra \mathfrak g and left invariant pseudo-Riemannian metric g generated by < , >.
(G,g) (or \mathfrak g,< , >) is said to be an algebraic Ricci soliton if its Ricci operator Ric=c Id+D for some constant real number c and D in Der(\mathfrak g).In the Riemannian case, algebraic Ricci solitons are well understood due to the results of Lauret. In this talk, we consider Lorentz algebraic Ricci solitons on nilpotent Lie groups.
Based on the concept of Lorentz datum and the technique of double extensions, we are able to construct Lorentz Ricci nilsolitons from any Riemannian Ricci nilsoliton.
Conversely, we show that any Lorentz Ricci nilsoliton with degenerate center is a double extension of a Riemannian Ricci nilsoliton with respect to a Lorentz data. Moreover, we provide a strategy to classify Lorentz Ricci nilsolitons with degenerate center. This is a joint work with S. Deng.