Vinberg's algorithm
Encyclopedia
In mathematics, Vinberg's algorithm is an algorithm, introduced by Ernest Borisovich Vinberg
, for finding a fundamental domain
of a hyperbolic reflection group.
used Vinberg's algorithm to describe the automorphism group of the 26-dimensional even unimodular Lorentzian lattice II25,1
in therms of the Leech lattice
.
Ernest Borisovich Vinberg
Ernest Borisovich Vinberg is a Russian mathematician, who works on discrete subgroups of Lie groups and representation theory. He introduced Vinberg's algorithm. He is a recipient of the Humboldt Prize.-References:*...
, for finding a fundamental domain
Fundamental domain
In geometry, the fundamental domain of a symmetry group of an object is a part or pattern, as small or irredundant as possible, which determines the whole object based on the symmetry. More rigorously, given a topological space and a group acting on it, the images of a single point under the group...
of a hyperbolic reflection group.
used Vinberg's algorithm to describe the automorphism group of the 26-dimensional even unimodular Lorentzian lattice II25,1
II25,1
In mathematics, II25,1 is the even 26-dimensional Lorentzian unimodular lattice. It has several unusual properties, arising from Conway's discovery that it has a norm zero Weyl vector...
in therms of the Leech lattice
Leech lattice
In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space E24 found by .-History:Many of the cross-sections of the Leech lattice, including the Coxeter–Todd lattice and Barnes–Wall lattice, in 12 and 16 dimensions, were found much earlier than...
.