affine group in a sentence
1) Two affine Coxeter groups can be multiplied together.
affine collocations
2) The affine group has a unitary irreducible representation on the Hilbert space __FORMULA__.
3) The affine Coxeter groups form a second important series of Coxeter groups.
affine group example sentences
4) Families of convex uniform Euclidean tessellations are defined by the affine Coxeter groups .5) Finite and affine groups are also called "elliptical" and "parabolic" respectively.
6) Here are all of the Dynkin graphs for affine groups up to 10 nodes.
7) For example, the left and right invariant Haar measures on the affine group are not equal.
8) Vanilla siteswap patterns may be viewed as certain elements of the affine Weyl group of type __FORMULA__.
9) A typical example of the above construction is provided by the affine group of the line, __FORMULA__.
10) Euclidean uniform honeycombs are generated by affine Coxeter groups and hyperbolic honeycombs are generated by the hyperbolic Coxeter groups.
11) The deRham decomposition theorem does not apply to affine holonomy groups , so a complete classification is out of reach.
12) Comparisons of figures in affine geometry are made with affinities, which are mappings comprising the affine group "A".
13) Similarly the Lie algebras of the linear group "AN" and the affine group "N"0 lie in __FORMULA__.
14) Representations for the Groups, and their Generators We now want a way to determine such a matrix representation of this affine group .
15) In the case of affine Coxeter groups like , or , one mirror, usually the last, is translated off the origin.
example sentences with affine group
16) There are 5 hyperbolic Coxeter groups expressing ideal simplices, graphs where removal of any one node results in an affine Coxeter group .17) This answers part of Hilbert's 18th problem. showed that conversely any group that is the extension of Z"n" by a finite group acting faithfully is an affine space group .
18) For each infinite family {"W""n"} of finite or affine Weyl groups , the rank of "M"("W") stabilizes as "n" goes to infinity.
19) When "W" is an affine Weyl group , the Coxeter complex is a subdivision of the affine plane and one speaks of affine, or Euclidean, buildings.
20) Oswald Veblen (1918) "Projective Geometry", volume 2, chapter 3: affine group in the plane, pp 70 to 118, Ginn & Company.
21) It is not the whole " affine group " because we must allow also translations by vectors "v" in "V".
22) The normalizer therefore has order "p"·("p"−1) and is known as a Frobenius group (especially for ), and is the affine general linear group , .
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