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  • 1
    Electronic Resource
    Electronic Resource
    On the Lie algebras generated by two two-forms in Minkowski space–time (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 5792-5804 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In relativity, planes and two-forms play important roles in the description of physical configurations or objects. When these configurations or objects interact, or are superposed, the corresponding planes or two-forms appear associated by pairs, and the relative position of the pair allows the classification of the particular form of the interaction. Here it is shown that in Minkowski space a pair of planes may adopt 35 relative positions. This result allows the almost complete characterization of the dimension of the Lie (sub)algebras (of the Lorentz group) generated by a pair of two-forms in terms of the relative position of their invariant planes. Furthermore, it is shown that, apart from Patera et al. algebras F2 and F5 (for which the eigenvalues' ratios have to be computed as well), the position of their invariant planes is also sufficient to determine the algebra itself generated by two two-forms. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531699
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  • 2
    Electronic Resource
    Electronic Resource
    On the commutator of two 2-forms in Minkowski space–time (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 4350-4362 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In the space–time of general relativity, 2-forms play several important roles. But their commutators are generally seen as elements related to their algebraic aspects, rather than to their geometric ones. Here a clear geometric meaning of the commutator of two 2-forms is given. To obtain it, some simple notions on the Minkowski tangent space are needed. The characteristic tetrad and the characteristic planes of two generic planes are introduced. For nongeneric planes (those that cut each other or coincide), the matrix of their intersections and of the intersections of their orthogonals is considered, and some of its properties analyzed. The orthogonal cut of a plane is defined and the planes that orthogonally cut two given planes are studied. These results allow one to relate very easily the invariant planes of the commutator of two 2-forms to the invariant planes of the 2-forms: the first ones are the single orthogonal cut of the last ones. Some applications are indicated. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530966
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    Paper (German National Licenses)
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