Hurwitz quaternion order and arithmetic Riemann surfaces

Mikhail G. Katz; Mary Schaps; Uzi Vishne

doi:10.1007/s10711-011-9582-3

Hurwitz quaternion order and arithmetic Riemann surfaces

Mikhail G. Katz, Mary Schaps, Uzi Vishne

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

We clarify the explicit structure of the Hurwitz quaternion order, which is of fundamental importance in Riemann surface theory and systolic geometry.

Original language	English
Pages (from-to)	151-161
Number of pages	11
Journal	Geometriae Dedicata
Volume	155
Issue number	1
DOIs	https://doi.org/10.1007/s10711-011-9582-3
State	Published - Dec 2011

Keywords

Arithmetic lattice
Azumaya algebras
Fuchsian group
Hurwitz group
Hurwitz order
Hyperbolic reflection group
Hyperbolic surface
Quaternion algebra
Subgroup growth
Systole

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.1007/s10711-011-9582-3

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title = "Hurwitz quaternion order and arithmetic Riemann surfaces",

abstract = "We clarify the explicit structure of the Hurwitz quaternion order, which is of fundamental importance in Riemann surface theory and systolic geometry.",

keywords = "Arithmetic lattice, Azumaya algebras, Fuchsian group, Hurwitz group, Hurwitz order, Hyperbolic reflection group, Hyperbolic surface, Quaternion algebra, Subgroup growth, Systole",

author = "Katz, {Mikhail G.} and Mary Schaps and Uzi Vishne",

note = "Funding Information: Acknowledgments M. G. Katz is supported by the Israel Science Foundation (grants no. 84/03 and 1294/06) and the Binational Science Foundation (grant 2006393). U. Vishne is supported by the EU research and training network HPRN-CT-2002-00287, ISF Center of Excellence grant 1405/05, and BSF grant no. 2004-083.",

year = "2011",

month = dec,

doi = "10.1007/s10711-011-9582-3",

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AU - Katz, Mikhail G.

AU - Schaps, Mary

AU - Vishne, Uzi

N1 - Funding Information: Acknowledgments M. G. Katz is supported by the Israel Science Foundation (grants no. 84/03 and 1294/06) and the Binational Science Foundation (grant 2006393). U. Vishne is supported by the EU research and training network HPRN-CT-2002-00287, ISF Center of Excellence grant 1405/05, and BSF grant no. 2004-083.

PY - 2011/12

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N2 - We clarify the explicit structure of the Hurwitz quaternion order, which is of fundamental importance in Riemann surface theory and systolic geometry.

AB - We clarify the explicit structure of the Hurwitz quaternion order, which is of fundamental importance in Riemann surface theory and systolic geometry.

KW - Arithmetic lattice

KW - Azumaya algebras

KW - Fuchsian group

KW - Hurwitz group

KW - Hurwitz order

KW - Hyperbolic reflection group

KW - Hyperbolic surface

KW - Quaternion algebra

KW - Subgroup growth

KW - Systole

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DO - 10.1007/s10711-011-9582-3

M3 - مقالة

SN - 0046-5755

VL - 155

SP - 151

EP - 161

JO - Geometriae Dedicata

JF - Geometriae Dedicata

IS - 1

ER -

Hurwitz quaternion order and arithmetic Riemann surfaces

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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