On Generating set of commutator of Casimir operator

• Main Author: 吳岳賜
• Other Authors: 杜子明
• Format: Others
• Language: en_US
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/60510594024933062027

碩士 === 國立彰化師範大學 === 數學系 === 87 === Let b=a\oplus u be the solvable Lie algebra,where a and u are commutative subalgebras,with u an ideal.Let \Omega =\sum {H_i}^2+\sum {X_j}^2, where {H_i } and {X_j}are orthonormal bases for a and u, respectively. Let sl_n= k\oplus a\oplus n be its Iwasawa decomposition, where k=so_n,a is the subalgebra consisting of diagonal matrices of trace zero,and n is the subalgebra consisting of nilpotent matrices. Set b=a\oplus n/[n,n]. In this paper, we find, for sl_n, a generating set of the centralizers of \Omega in U(b), where U(b) is the universal enveloping algebra of b.