Generalized Euler decompositions of some six-dimensional Lie groups

Here we present the generalized Euler decompositions of the six-dimensional Lie groups SO(4), SO*(4) and SO(2,2) using their (local) direct product structure [1] and a technique we have developed for SO(3) and SO(2,1) (cf. [2]). Although in even dimensions the Euler invariant axis theorem is not val...

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Bibliographic Details
Main Authors: Brezov, Danail S, Mladenova, Clementina D, Mladenov, Ivaïlo M
Format: Conference Proceeding
Language:English
Subjects:
Axes (reference lines)
Decomposition
Lie groups
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Summary:Here we present the generalized Euler decompositions of the six-dimensional Lie groups SO(4), SO*(4) and SO(2,2) using their (local) direct product structure [1] and a technique we have developed for SO(3) and SO(2,1) (cf. [2]). Although in even dimensions the Euler invariant axis theorem is not valid, one may introduce the notion of bi-axis n ⊗ ñ and decompose the generalized vector-parameter c ⊗ c̃ with respect to a given set of bi-axes. As for the Lorentz group SO(3,1), we deal with complex vector-parameters [4] and the decomposition intertwines real and imaginary parts of vectors. Thus, bi-axes in that case have the interpretation of projective lines in parameter space CP3.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.4902488