E8 lattice

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the E8 lattice is a special <a href="/facts/Lattice_(group)/2ls9Iv9N">lattice</a> in R8. It can be characterized as the unique positive-definite, even, <a href="/facts/Unimodular_lattice/6r8l4y81">unimodular lattice</a> of rank 8. The name derives from the fact that it is the <a href="/facts/Root_lattice/TFaEdwMU">root lattice</a> of the <a href="/facts/E8_(mathematics)/NEaKT71H">E8 root system</a>.
</p><p>The norm of the E8 lattice (divided by 2) is a positive definite even unimodular <a href="/facts/Quadratic_form/l2n1jXPe">quadratic form</a> in 8 variables, and conversely such a quadratic form can be used to construct a positive-definite, even, <a href="/facts/Unimodular_lattice/6r8l4y81">unimodular lattice</a> of rank 8.
The existence of such a form was first shown by <a href="/facts/H._J._S._Smith/sD12Jf6L">H. J. S. Smith</a> in 1867, and the first explicit construction of this quadratic form was given by <a href="/facts/Aleksandr_Korkin/3oNhWrly">Korkin</a> and <a href="/facts/Yegor_Ivanovich_Zolotarev/pCXfRy4x">Zolotarev</a> in 1873.
The E8 lattice is also called the Gosset lattice after <a href="/facts/Thorold_Gosset/3wvHtGPn">Thorold Gosset</a> who was one of the first to study the geometry of the lattice itself around 1900.
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E8 lattice open-in-new

E8 lattice