| Summary: | 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.
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