Classification of stably reflective hyperbolic \(\mathbb{Z}[\sqrt 2 ]\)-lattices of rank 4

DOI10.1134/S1064562419030013zbMath1444.11149MaRDI QIDQ2332077

N. V. Bogachev

Publication date: 1 November 2019

Published in: Doklady Mathematics (Search for Journal in Brave)

zbMATH Keywords

Lobachevsky spacestably reflective hyperbolic \(\mathbb{Z}[\sqrt 2 \)-lattices]

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Quadratic forms over global rings and fields (11E12) Reflection groups, reflection geometries (51F15) Quadratic forms (reduction theory, extreme forms, etc.) (11H55)

Uses Software

• GitHub
• vinberg-algorithm
• VinAlg-Z-sqrt-2

Cites Work

• Unnamed Item
• Finiteness of arithmetic hyperbolic reflection groups
• Vinberg's algorithm for hyperbolic lattices
• Arithmetic hyperbolic reflection groups
• Classification of $(1{,}{\kern1pt}2)$-reflective anisotropic hyperbolic lattices of rank $4$
• Reflective anisotropic hyperbolic lattices of rank 4
• Finiteness of the number of arithmetic groups generated by reflections in Lobachevsky spaces
• ON GROUPS OF UNIT ELEMENTS OF CERTAIN QUADRATIC FORMS