Vinberg's Algorithm for Hyperbolic Lattices

Богачев, Николай Владимирович; Nikolay, Bogachev,; Перепечко, Александр Юрьевич; Perepechko, Aleksander Yur'evich

doi:10.4213/mzm11889

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метод наиболее удалённого ребра1

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2019

2023

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Cited by 6 publications

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“…где G ij -алгебраические дополнения матрицы G u u u u ( , , , Отметим, что в 2017 г. автор совместно с А. Ю. Перепечко написал программу для произвольных решёток над Z [15], её подробное описание см. в [5].…”

Section: метод наиболее удалённого ребраunclassified

On the classification of stably reflective hyperbolic Z[√2]-lattices of rank 4

Nikolay

2019

Доклады Академии наук

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Section: метод наиболее удалённого ребраunclassified

On the classification of stably reflective hyperbolic Z[√2]-lattices of rank 4

Nikolay

2019

Доклады Академии наук

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From Geometry to Arithmetic of Compact Hyperbolic Coxeter Polytopes

Nikolay

2022

Transformation Groups

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In 1974, Kaplinskaja classified all simplicial straight hyperbolic Coxeter prisms. In this paper, we determine precisely which of these prisms are properly quasi-arithmetic or arithmetic. We also present some observations regarding commensurability classes and systoles of the associated orbifolds. Finally, we show that there is a cocompact properly quasi-arithmetic reflection group in H 3 preserving an isotropic quadratic form. This phenomenon was previously known due to Vinberg only in dimension 2.

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Classification of $(1{,}{\kern1pt}2)$-reflective anisotropic hyperbolic lattices of rank $4$

Nikolay¹

2019

Izv. Math.

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Vinberg's Algorithm for Hyperbolic Lattices

Cited by 6 publications

References 6 publications

On the classification of stably reflective hyperbolic Z[√2]-lattices of rank 4

On the classification of stably reflective hyperbolic Z[√2]-lattices of rank 4

From Geometry to Arithmetic of Compact Hyperbolic Coxeter Polytopes

Classification of $(1{,}{\kern1pt}2)$-reflective anisotropic hyperbolic lattices of rank $4$

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