caa a22 4500 445836105 CHVBK 20180317145330.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00209-009-0643-3 doi (NATIONALLICENCE)springer-10.1007/s00209-009-0643-3 New HKT manifolds arising from quaternionic representations [Elektronische Daten] [M. Barberis, A. Fino] We give a procedure for constructing an 8n-dimensional HKT Lie algebra starting from a 4n-dimensional one by using a quaternionic representation of the latter. The strong (respectively, weak, hyper-Kähler, balanced) condition is preserved by our construction. As an application of our results we obtain a new compact HKT manifold with holonomy in $${SL(n,\mathbb{H})}$$ which is not a nilmanifold. We find in addition new compact strong HKT manifolds. We also show that every Kähler Lie algebra equipped with a flat, torsion-free complex connection gives rise to an HKT Lie algebra. We apply this method to two distinguished 4-dimensional Kähler Lie algebras, thereby obtaining two conformally balanced HKT metrics in dimension 8. Both techniques prove to be an effective tool for giving the explicit expression of the corresponding HKT metrics. Springer-Verlag, 2009 Barberis M. FaMAF-CIEM, Universidad Nacional de Córdoba, 5000, Córdoba, Argentina aut Fino A. Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123, Torino, Italy aut Mathematische Zeitschrift Springer-Verlag 267/3-4(2011-04-01), 717-735 0025-5874 267:3-4<717 2011 267 209 https://doi.org/10.1007/s00209-009-0643-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-009-0643-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Barberis M. FaMAF-CIEM, Universidad Nacional de Córdoba, 5000, Córdoba, Argentina aut NATIONALLICENCE 700 1- Fino A. Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123, Torino, Italy aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 267/3-4(2011-04-01), 717-735 0025-5874 267:3-4<717 2011 267 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer