Some Results on the Classification of Triple Systems |
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Page 50
... ge Gona e A by ao . If A is a G - group , we define the group AG by z1 AG and the set Z ( G , A ) by : = { a € A | a8 = a for all ge G } z1 ( G , A ) : = { n : G → A | n ( gh ) n ... G Nevertheless , and so we can say a sequence H1 ( G 50.
... ge Gona e A by ao . If A is a G - group , we define the group AG by z1 AG and the set Z ( G , A ) by : = { a € A | a8 = a for all ge G } z1 ( G , A ) : = { n : G → A | n ( gh ) n ... G Nevertheless , and so we can say a sequence H1 ( G 50.
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... a short exact sequence of G - groups . ( i ) Then the following sequence of sets is exact : В * 1 → A Ga G B B ၉၆ G 6 H1 ( G , A ) H1 ( G , B ) Η B2 H2 ( G , C ) = an ( g ) for all g e G , B is defined = C. where a ( [ n ] ) = [ n ' ] ...
... a short exact sequence of G - groups . ( i ) Then the following sequence of sets is exact : В * 1 → A Ga G B B ၉၆ G 6 H1 ( G , A ) H1 ( G , B ) Η B2 H2 ( G , C ) = an ( g ) for all g e G , B is defined = C. where a ( [ n ] ) = [ n ' ] ...
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... ( G , K ** K * ) = 1 for all choices of M , Recall that by ( 5.9 ) T ge G where a50 Ο ( 8 ) 1ta ( g ) for t e Aut ( § ; o ) and g = as ( 8 ) 1ras ( g ) is the g - semilinear automorphism of S which is the identity on So 3 。= M。® R ( Mo ...
... ( G , K ** K * ) = 1 for all choices of M , Recall that by ( 5.9 ) T ge G where a50 Ο ( 8 ) 1ta ( g ) for t e Aut ( § ; o ) and g = as ( 8 ) 1ras ( g ) is the g - semilinear automorphism of S which is the identity on So 3 。= M。® R ( Mo ...
Common terms and phrases
a e k algebra system Aut L yes Aut S,o Aut*L automorphism groups bijective correspondence bilinear form central subgroup Chapter characteristic zero classes of k-forms classes of polarized Corollary 4.12 correspondence between elements dim ker direct sum dual Dynkin diagram elements of H¹(G exact sequences Faulkner diagram finite dimensional follows from Lemma G-group Galois descent Galois group H¹ G Hence homomorphism inner derivations irreducible components irreducible L-modules irreducible submodules Jordan pair Jordan triple system k-isomorphism k-scalar isomorphism classes Lie algebra Lie module triple Lie triple systems M₁ and M₂ M₁ M₂ M₁t M₂ with M₁ module triple system nonassociative algebra nondegenerate nonzero normal subgroup polarized k-forms Proof R(M₁ R(M₁,M₂ R(M₂ scalar Schur's lemma semisimple simple Lie triple standard embedding subalgebra subgroup of Aut submodules Suppose triple product twisted Lie module x,y e x₁ yes Aut απ ε ε