On semi-direct extensions of the Heisenberg group

• Autores: Giovanni Calvaruso
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 72, Fasc. 1, 2021, págs. 1-23
• Idioma: inglés
• DOI: 10.1007/s13348-019-00277-y
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• Resumen

  • Any S∈sp(1,R) induces canonically a derivation S of the Heisenberg Lie algebra h and so, a semi-direct extension GS=H⋊exp(RS) of the Heisenberg Lie group H (Müller and Ricci in Invent Math 101: 545–582, 1990). We shall explicitly describe the connected, simply connected Lie group GS and a family ga of left-invariant (Lorentzian and Riemannian) metrics on GS, which generalize the case of the oscillator group. Both the Lie algebra and the analytic description will be used to investigate the geometry of (GS,ga), with particular regard to the study of nontrivial Ricci solitons.