International Journal of Mathematics and Computational Science
Articles Information
International Journal of Mathematics and Computational Science, Vol.3, No.1, Feb. 2017, Pub. Date: Aug. 1, 2017
Invariant Differential Operator on Homogeneous Space
Pages: 1-5 Views: 191 Downloads: 88
[01] Maria Akter, Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh.
[02] Salma Nasrin, Department of Mathematics, University of Dhaka, Dhaka, Bangladesh.
This paper is the study of invariant differential operator on homogeneous space. We study how a manifold structure for the quotient group of a Lie group can be seen as a homogeneous space and the invariant differential operator on homogeneous space is commutative when homogeneous space symmetric.
Lie Group, Lie Algebra, Isotropy Group, Manifold, PBW Theorem and Symmetric Space
[01] Anthony W. Knapp, Lie Groups Beyond an Introduction (Second Edition), New York, 2002.
[02] Gerrit Heckman, Henrick Schlichtkrull, Harmonic Analysis And Special Functions on Sym-metric Spaces.
[03] Shlomo Sternberg, Lie Algebras, April 23, 2004.
[04] Warner, Frank W, Foundations of Differential Manifolds and Lie Groups, New York, 1983.
[05] M. P. DoCarmo, Riemannian Geometry, Birkha ̈user, 1972.
[06] J. Jost, Riemannian Geometry and Geometric Analysis, Universitext, Springer (2002).
[07] S. Helgason, Analysis on Lie groups and homogeneous space (Regional Conference series in Mathematics 14), Amer. Math. Soc. Providence, Rhode Island, 1972.
[08] J. Jacobson and H. Stetker, Eigenspace representation of nilpotent Lie groups, Math. Scand. (1981).
[09] Tuong Ton-That, Poincaré–Birkhoff–Witt theorems and generalized Casimir invariants for some infinite-dimensional Lie groups: II, Journal of Physics A: Mathematical and General, Volume 38, Number 4, 2005.
[10] Nguyen Huu Anh and Vuong Manh Son, Enveloping algebra of Lie groups with discrete series, Pacific journal of Mathematics 156 (1), November 1992.
[11] G. D Mostow, Discrete subgroups of lie groups, Advanced in Mathematics, Volume 16, Issue 1, April 1975.
[12] Philip Feinsilver and René Schott, Computing Representations of a Lie Group via the Universal Algebra, Journal of Symbolic Computation, Volume 26, Issue 3, 1998.
[13] Pulak Ranjan Giri, Non-commutativity as a measure of inequivalent quantization, Journal of Physics A: Mathematical and Theoretical, Volume 42, Number 35, 2009.
[14] E Celeghini, A Ballesteros and M A del Olmo, From quantum universal enveloping algebras, Journal of Physics A: Mathematical and Theoretical, Volume 41, Number 30, 2008.
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