Volume 28, Issue 2, January 2017, Pages 152–155
Gregoire Lutanda Panga1, Patricka Azere Phiri2, and Philippe Muyumba Kabwita3
1 Department of Mathematics-Informatics, Faculty of Sciences, University of Lubumbashi, RD Congo
2 Department of Mathematics, Copperbelt University, Zambia
3 Department of Physics, Copperbelt University, Zambia
Original language: English
Copyright © 2017 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper, we consider the de Sitter algebra and we realize the Kählerian structure by using the fact that the dual of a Lie algebra of a Lie group has a natural Poisson structure and also the fact that a non-degenerate Killing form on a Lie algebra induces a metric on its dual.
Author Keywords: Lie algebra of Lie group, Kirillov form, Killing form, Poisson bracket, Riemann bracket, Hermitian metric, Kähler manifold.
Gregoire Lutanda Panga1, Patricka Azere Phiri2, and Philippe Muyumba Kabwita3
1 Department of Mathematics-Informatics, Faculty of Sciences, University of Lubumbashi, RD Congo
2 Department of Mathematics, Copperbelt University, Zambia
3 Department of Physics, Copperbelt University, Zambia
Original language: English
Copyright © 2017 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this paper, we consider the de Sitter algebra and we realize the Kählerian structure by using the fact that the dual of a Lie algebra of a Lie group has a natural Poisson structure and also the fact that a non-degenerate Killing form on a Lie algebra induces a metric on its dual.
Author Keywords: Lie algebra of Lie group, Kirillov form, Killing form, Poisson bracket, Riemann bracket, Hermitian metric, Kähler manifold.
How to Cite this Article
Gregoire Lutanda Panga, Patricka Azere Phiri, and Philippe Muyumba Kabwita, “Kählerian structure associated to de Sitter group,” International Journal of Innovation and Scientific Research, vol. 28, no. 2, pp. 152–155, January 2017.
