We describe the correlations between Gram determinantdetG(x1, . . . , xm)of thesystem{x1, . . . , xm}and the number of linearly independent null vectors in the system{x1, . . . , xm}.Using methods of invariant theory and these results, the system of generators of the polynomialring of allG-invariant polynomial functions of vectorsx, x2, . . . , xminEn1is obtained for groupsG = M (n, 1)andG = SM (n, 1).
📌 3 Maddede Bu Makale
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Amaç & Hipotez:LetGbe the groupM (n, 1)generated by all pseudo-orthogonal transformations and translationsof Lorentzian spaceEn1orG = SM (n, 1)is the subgroup ofM (n, 1)generated by rotations andtranslations ofEn1.
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Temel Bulgular & Veri:LetGbe the groupM (n, 1)generated by all pseudo-orthogonal transformations and translationsof Lorentzian spaceEn1orG = SM (n, 1)is the subgroup ofM (n, 1)generated by rotations andtranslations ofEn1.
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Sonuç & Katkı:We describe the correlations between Gram determinantdetG(x1, . . . , xm)of thesystem{x1, . . . , xm}and the number of linearly independent null vectors in the system{x1, . . . , xm}.Using methods of invariant theory and these results, the system of generators of the polynomialring of allG-invariant polynomial functions of vectorsx, x2, . . . , xminEn1is obtained for groupsG = M (n, 1)andG = SM (n, 1).
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri
Abstract
LetGbe the groupM (n, 1)generated by all pseudo-orthogonal transformations and translationsof Lorentzian spaceEn1orG = SM (n, 1)is the subgroup ofM (n, 1)generated by rotations andtranslations ofEn1. We describe the correlations between Gram determinantdetG(x1, . . . , xm)of thesystem{x1, . . . , xm}and the number of linearly independent null vectors in the system{x1, . . . , xm}.Using methods of invariant theory and these results, the system of generators of the polynomialring of allG-invariant polynomial functions of vectorsx, x2, . . . , xminEn1is obtained for groupsG = M (n, 1)andG = SM (n, 1).
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Bu Makaleye Atıf Yap
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