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Graph parameters and invariants of the orthogonal group
Regts, G.
Publication date
2013
Link to publication
Citation for published version (APA):
Regts, G. (2013). Graph parameters and invariants of the orthogonal group.
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Index
affine variety, 29 quasi–, 67 algebra Brauer–, 31 contraction-closed–, 57 fragment–, 54 graph–, 13 group–, 25 homomorphism, 13 labeled graph–, 60 quotient–, 13 semigroup–, 13 semisimple–, 32 tensor–, 54 canonical basis, 73 compact orbit space, 85 weakly–, 86 completely reducible, 26 connection matrix, 11 edge–, 11 vertex–, 11 contraction, 20, 55 closed, 56 labeled–, 62 convergent graph sequence, 84sequence of edge-coloring models, 84
degree, 8
edge-coloring model, 17 C-color–, 88
k-color–, 19
convergent sequence of–, 84 finite rank–, 38
nondegenerate–, 55
partition function of an–, 19 rank of an–, 36
real–, 19 equivariant, 25
First Fundamental Theorem, 27 fragment l- –, 9 quantum–, 54 gluing operation, 10 gluing product, 9 graded, 56 graph, 8 l-labeled quantum–, 12 l-labeled–, 8 algebra, 13 dense–, 83 directed–, 50 homomorphism, 18 invariant, 8 line–, 20 109
INDEX parameter, 8 directed–, 50 quantum–, 13 simple–, 8 graphon, 84 group action, 25 affine algebraic–, 29 automorphism–, 51 linear algebraic–, 29 orthogonal–, 21, 89 reductive–, 29 stabilizer–, 57 symmetric–, 30 half edge, 9 Hilbert space, 86 Hilbert-Mumford, 73 homomorphism density, 84 natural–, 54 of algebraic groups, 73 of algebras, 13 of graphs, 18 of groups, 25 of linegraphs, 19 invariant G- –, 26 Ok- –, 56 graph–, 8 theory, 25 Ising model, 16 module, 25 moment matrix, 36 multiplicative, 11 nondegenerate edge-coloring model, 55 linear space, 71 matrix, 71
symmetric bilinear form, 20 vertex-coloring model, 61 Nullstellensatz, 29 open edge, 10 open end, 9 orbit space, 86 orthogonal group, 21 partition function, 16 directed–, 50 of a graphon, 84 of a vertex-coloring model, 17 of an edge-coloring model, 19, 88 perfect matching, 19 product, 11 pseudometric, 86 quotient map, 30 rank, 8, 36 reductive, 29 reflection positive, 12 edge- –, 12 representation, 25 Reynolds operator, 26
Second Fundamental Theorem, 27 seminorm, 86 spin model, 16 stable, 25 subgroup one-parameter–, 73 Tensor FFT, 27 tensor network, 20 twin, 18 free, 18 vertex model, 17 110
INDEX
vertex-coloring model, 17 n-color–, 17
nondegenerate–, 61 partition function of a–, 17 real–, 17
weight, 74 Zariski closed, 29