Vinberg's algorithm

In mathematics, Vinberg's algorithm is an algorithm, introduced by Ernest Borisovich Vinberg, for finding a fundamental domain of a hyperbolic reflection group. ^[1]

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Table of Contents

1. 7 relations: Coxeter–Dynkin diagram, Ernest Vinberg, Fundamental domain, II25,1, Journal of Algebra, Leech lattice, Oxford University Press.

2. Reflection groups

Coxeter–Dynkin diagram

In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing a Coxeter group or sometimes a uniform polytope or uniform tiling constructed from the group.

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Ernest Vinberg

Ernest Borisovich Vinberg (Эрне́ст Бори́сович Ви́нберг; 26 July 1937 – 12 May 2020) was a Soviet and Russian mathematician, who worked on Lie groups and algebraic groups, discrete subgroups of Lie groups, invariant theory, and representation theory.

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Fundamental domain

Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action.

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II25,1

In mathematics, II25,1 is the even 26-dimensional Lorentzian unimodular lattice.

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Journal of Algebra

Journal of Algebra (ISSN 0021-8693) is an international mathematical research journal in algebra.

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Leech lattice

In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space, which is one of the best models for the kissing number problem.

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Oxford University Press

Oxford University Press (OUP) is the publishing house of the University of Oxford.

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See also

Reflection groups

• Affine symmetric group
• Complex reflection group
• Coxeter group
• Descent algebra
• Mirrors and Reflections
• Parabolic subgroup of a reflection group
• Reflection group
• Vinberg's algorithm

References

[1] https://en.wikipedia.org/wiki/Vinberg's_algorithm

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