In geometry and mathematical group theory, a unimodular lattice is an integral lattice of determinant 1 or −1. For a lattice in n-dimensional Euclidean space, this is equivalent to requiring that the volume of any fundamental domain for the lattice be 1.
The E8 lattice and the Leech lattice are two famous examples.
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geometry and mathematical group theory, a unimodularlattice is an integral lattice of determinant 1 or −1. For a lattice in n-dimensional Euclidean space, this...
mathematics, the E8 lattice is a special lattice in R8. It can be characterized as the unique positive-definite, even, unimodularlattice of rank 8. The name...
In mathematics, the Leech lattice is an even unimodularlattice Λ24 in 24-dimensional Euclidean space, which is one of the best models for the kissing...
mathematics, unimodular may refer to any of the following: UnimodularlatticeUnimodular matrix Unimodular polynomial matrix Unimodular form Unimodular group...
In mathematics, a Niemeier lattice is one of the 24 positive definite even unimodularlattices of rank 24, which were classified by Hans-Volker Niemeier (1973)...
of a root lattice. The integer lattice is an odd unimodularlattice. The automorphism group (or group of congruences) of the integer lattice consists of...
unimodular matrix used (possibly implicitly) in lattice reduction and in the Hermite normal form of matrices. The Kronecker product of two unimodular...
only one even unimodularlattice in 15 dimensions or less — the E8 lattice. Up to dimension 24, there is only one even unimodularlattice without roots...
E 8 {\displaystyle \mathrm {E} _{8}} lattice Γ8 is the smallest positive even unimodularlattice. As a lattice, it holds the optimal structure for the...
identically zero. II. Theta functions of even unimodularlattices An even unimodularlattice L in Rn is a lattice generated by n vectors forming the columns...
Kac–Moody algebra which has the even Lorentzian unimodularlattice II9,1 of dimension 10 as its root lattice. It is the first E n {\displaystyle \mathrm {E}...
function of a lattice is then a holomorphic function on the upper half-plane. Furthermore, the theta function of an even unimodularlattice of rank n is...
an integral lattice, det ( L ) 2 = | L ∗ / L | {\textstyle {\text{det}}(L)^{2}=|L^{*}/L|} . An integral lattice is said to be unimodular if L = L ∗ {\textstyle...
Bust Niven's constant See list of algebraic number theory topics Unimodularlattice Fermat's theorem on sums of two squares Proofs of Fermat's theorem...
similarly for the others. The theta function of an eight-dimensional even unimodularlattice Γ is a modular form of weight 4 for the full modular group, which...
with values in the integers, known as the K3 lattice. This is isomorphic to the even unimodularlattice II 3 , 19 {\displaystyle \operatorname {II} _{3...
Picard group is the odd unimodularlattice I1,n, except for the Hirzebruch surfaces Σ2m when it is the even unimodularlattice II1,1. Guido Castelnuovo...
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