Published: 1983 Received: September 07, 1981Available on J-STAGE: October 20, 2006Accepted: -
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Date of correction: October 20, 2006Reason for correction: -Correction: CITATIONDetails: Wrong : 1) L. Auslander and C. C. Moore, Unitary representations of solvable Lie groups, Mem. Amer. Math. Soc., 62 (1966). 2) F. Combes, Poids sur une C*-algebre, J. Math. Pure Appl., 47 (1968), 57-100. 3) E. G. Ernest, A decomposition theory for unitary representations of locally compact group, Trans. Amer. Math. Soc., 104 (1962), 252-277. 4) E. G. Ernest, A strong duality theorem for separable locally compact groups, Trans. Amer. Math. Soc., 156 (1971), 287-308. 5) S. Funakoshi, On representations of non type I groups, Tohoku Math. J., 31 (1979), 139-150. 6) E. C. Gootman and J. Rosenberg, The structure of crossed product C*-algebras: a proof of the generalized Effros-Hahn conjecture, Invent. Math., 102 (1979), 283-298. 7) H. Halpern, Quasi-equivalence class of normal representations for a separable C*-algebras, Trans. Amer. Math. Soc., 203 (1975), 129-140. 8) K. Ikeshoji and Y. Nakagami, On a strong duality for separable locally compact groups, Mem. Kyushu Univ., 33 (1979), 377-389. 9) S. Kawakami, On representations of Heisenberg type groups, Master Thesis, (in Japanese). 10) J. Kallman, A generalization of free action, Duke Math. J., 36 (1969) , 781-789. 11) A. Kleppner, Continuity and measurability of multiplier and projective representations, J. Functional Analysis, 17 (1974), 214-226. 12) A. Kleppner and R. L. Lipsman, Plancherel formula for group extensions, Ann. Sci. École Norm. Sup., 5 (1972), 459-516. 13) A. Kleppner and R. L. Lipsman, Plancherel formula for group extensions II, Ann. Sci. École Norm. Sup., 6 (1973), 103-132. 14) G. W. Mackey, Unitary representation of group extensions I, Acta Math., 99 (1958), 263-311. 15) G. K. Pedersen and M. Takesaki, The Radon Nikodym theorem for von Neumann algebras, Acta Math., 130 (1973), 53-88. 16) N. V. Pedersen, Semicharacters and solvable Lie groups, Math. Ann., 247 (1980), 191-244. 17) N. V. Pedersen, Semicharacters on connected Lie groups, preprint, Univ. of Copenhagen. 18) L. Pukanszky, Unitary representations of solvable Lie groups, Ann. Sci. École Norm. Sup., 4 (1971), 457-608. 19) L. Pukanszky, Characters of connected Lie groups, Acta Math., 133 (1974), 81-137. 20) J. C. Quigg, On irreducibility of an induced representation, Pacific J. Math., 93 (1981), 163-179. 21) C. E. Sutherland, The direct integral theory of weights and Plancherel formula, Thesis, UCLA, 1973. 22) N. Tatsuuma, Plancherel formula for non-unimodular locally compact groups, J. Math. Kyoto Univ., 12 (1972), 179-261. 23) G. W. Mackey, Induced representations of locally compact groups I, Ann. of Math., 55 (1952), 101-139.
Right : [1] L. Auslander and C. C. Moore, Unitary representations of solvable Lie groups, Mem. Amer. Math. Soc., 62 (1966). [2] F. Combes, Poids sur une C-algebre, J. Math. Pure Appl., 47 (1968), 57-100. [3] E. G. Ernest, A decomposition theory for unitary representations of locally compact group, Trans. Amer. Math. Soc., 104 (1962), 252-277. [4] E. G. Ernest, A strong duality theorem for separable locally compact groups, Trans. Amer. Math. Soc., 156 (1971), 287-308. [5] S. Funakoshi, On representations of non type I groups, Tôhoku Math. J., 31 (1979), 139-150. [6] E. C. Gootman and J. Rosenberg, The structure of crossed product C-algebras: a proof of the generalized Effros-Hahn conjecture, Invent. Math., 102 (1979), 283-298. [7] H. Halpern, Quasi-equivalence class of normal representations for a separable C-algebras, Trans. Amer. Math. Soc., 203 (1975), 129-140. [8] K. Ikeshoji and Y. Nakagami, On a strong duality for separable locally compact groups, Mem. Kyushu Univ., 33 (1979), 377-389. [9] S. Kawakami, On representations of Heisenberg type groups, Master Thesis, (in Japanese). [10] J. Kallman, A generalization of free action, Duke Math. J., 36 (1969), 781-789. [11] A. Kleppner, Continuity and measurability of multiplier and projective representations, J. Functional Analysis, 17 (1974), 214-226. [12] A. Kleppner and R. L. Lipsman, Plancherel formula for group extensions, Ann. Sci. École Norm. Sup., 5 (1972), 459-516. [13] A. Kleppner and R. L. Lipsman, Plancherel formula for group extensions II, Ann. Sci. École Norm. Sup., 6 (1973), 103-132. [14] G. W. Mackey, Unitary representation of group extensions I, Acta Math., 99 (1958), 263-311. [15] G. K. Pedersen and M. Takesaki, The Radon Nikodym theorem for von Neumann algebras, Acta Math., 130 (1973), 53-88. [16] N. V. Pedersen, Semicharacters and solvable Lie groups, Math. Ann., 247 (1980), 191-244. [17] N. V. Pedersen, Semicharacters on connected Lie groups, preprint, Univ. of Copenhagen. [18] L. Pukanszky, Unitary representations of solvable Lie groups, Ann. Sci. École Norm. Sup., 4 (1971), 457-608. [19] L. Pukanszky, Characters of connected Lie groups, Acta Math., 133 (1974), 81-137. [20] J. C. Quigg, On irreducibility of an induced representation, Pacific J. Math., 93 (1981), 163-179. [21] C. E. Sutherland, The direct integral theory of weights and Plancherel formula, Thesis, UCLA, 1973. [22] N. Tatsuuma, Plancherel formula for non-unimodular locally compact groups, J. Math. Kyoto Univ., 12 (1972), 179-261. [23] G. W. Mackey, Induced representations of locally compact groups I, Ann. of Math., 55 (1952), 101-139.
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