Titlebook: Elements of the Theory of Representations; Aleksandr A. Kirillov Book 1976 Springer-Verlag Berlin Heidelberg 1976 Darstellung.Group repres

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Lie Groups and Lie AlgebrasAs we pointed out in 6.2, there are exactly two simple real Lie algebras of dimension 3. These are: the algebra . of real matrices of the second order with zero trace and the algebra . of real skew-symmetric matrices of thethird order.

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Examples of Wild Lie GroupsWe can construct a very simple example of a Lie group not belonging to type [[I]] as follows. Let α be an irrational real number. Consider the group [[G]] of matrices of the form

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Hirohisa Narita,Nelfa Desmira,Hideo Fujimotofirst chapters of the textbooks of A.N. Kolmogorov and S.V. Fomin [38] and of G. E. Silov [49].) One can find more penetrating treatments (including an exact definition of the concept of set) in the books of Fraenkel and Bar-Hillel [17] and P. Cohen [12].

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