Negative Ricci curvature on some non-solvable Lie groups
Sign Up to like & getrecommendations! Published in 2017 at "Geometriae Dedicata"
DOI: 10.1007/s10711-016-0185-x
Abstract: We show that for any non-trivial representation $$(V, \pi )$$(V,π) of $$\mathfrak {u}(2)$$u(2) with the center acting as multiples of the identity, the semidirect product $$\mathfrak {u}(2) \ltimes _\pi V$$u(2)⋉πV admits a metric with negative… read more here.
Keywords: metric negative; negative ricci; solvable lie; ricci curvature ... See more keywords
Left invariant Riemannian metrics with harmonic curvature are Ricci-parallel in solvable Lie groups and Lie groups of dimension ≤6
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Geometry and Physics"
DOI: 10.1016/j.geomphys.2022.104517
Abstract: We show that any left invariant metric with harmonic curvature on a solvable Lie group is Ricciparallel. We show the same result for any Lie group of dimension ≤ 6. read more here.
Keywords: lie; left invariant; lie groups; solvable lie ... See more keywords
Applying matrix theory to classify real solvable Lie algebras having 2-dimensional derived ideals
Sign Up to like & getrecommendations! Published in 2020 at "Linear Algebra and its Applications"
DOI: 10.1016/j.laa.2019.11.031
Abstract: Abstract We present a new approach to the problem of classifying real solvable Lie algebras having 2-dimensional derived ideals. Partial results on this problem were obtained by Schobel in 1993 and by Janisse in 2010.… read more here.
Keywords: algebras dimensional; real solvable; derived ideals; solvable lie ... See more keywords
Vanishing of cohomology and parameter rigidity of actions of solvable Lie groups, II
Sign Up to like & getrecommendations! Published in 2020 at "Ergodic Theory and Dynamical Systems"
DOI: 10.1017/etds.2020.97
Abstract: Abstract Let $M\stackrel {\rho _0}{\curvearrowleft }S$ be a $C^\infty $ locally free action of a connected simply connected solvable Lie group S on a closed manifold M. Roughly speaking, $\rho _0$ is parameter rigid if… read more here.
Keywords: solvable lie; parameter rigidity; vanishing cohomology; parameter ... See more keywords
Ideals and conjugacy classes in solvable lie algebras
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DOI: 10.1142/s021988782350202x
Abstract: A constructive procedure is given to determine all ideals of a solvable Lie algebra. This is used in determining algorithmically all conjugacy classes of subalgebras of a given solvable Lie algebra. read more here.
Keywords: classes solvable; conjugacy classes; lie algebras; solvable lie ... See more keywords
Solvable Lie and Leibniz superalgebras with a given nilradical
Sign Up to like & getrecommendations! Published in 2020 at "Forum Mathematicum"
DOI: 10.1515/forum-2020-0031
Abstract: Abstract Throughout this paper we show that under certain conditions the method for describing solvable Leibniz (resp. Lie) algebras with given nilradical by means of non-nilpotent outer derivations of the nilradical is also applicable to… read more here.
Keywords: leibniz superalgebras; lie; solvable lie; given nilradical ... See more keywords
Simply transitive NIL-affine actions of solvable Lie groups
Sign Up to like & getrecommendations! Published in 2021 at "Forum Mathematicum"
DOI: 10.1515/forum-2020-0114
Abstract: Abstract Every simply connected and connected solvable Lie group ???? admits a simply transitive action on a nilpotent Lie group ???? via affine transformations. Although the existence is guaranteed, not much is known about which… read more here.
Keywords: lie group; lie; simply transitive; solvable lie ... See more keywords