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Fungrim entry: 094772

Symbol: SL2Z — SL⁡2(Z)\operatorname{SL}_2(\mathbb{Z}) — Modular group
Whether SL⁡2(Z)\operatorname{SL}_2(\mathbb{Z}) or PSL⁡2(Z)\operatorname{PSL}_2(\mathbb{Z}) should be called "the modular group" is an arbitrary convention. Here we allow any element of SL⁡2(Z)\operatorname{SL}_2(\mathbb{Z}) to represent an element of the modular group, but we use PSL⁡2(Z)\operatorname{PSL}_2(\mathbb{Z}) when uniqueness is desired.
Definitions:
Fungrim symbol Notation Short description
SL2ZSL⁡2(Z)\operatorname{SL}_2(\mathbb{Z}) Modular group
PSL2ZPSL⁡2(Z)\operatorname{PSL}_2(\mathbb{Z}) Modular group (canonical representatives)
Source code for this entry:
Entry(ID("094772"),
    SymbolDefinition(SL2Z, SL2Z, "Modular group"),
    Description("Whether", SL2Z, "or", PSL2Z, "should be called \"the modular group\" is an arbitrary convention. Here we allow any element of", SL2Z, "to represent an element of the modular group, but we use", PSL2Z, "when uniqueness is desired."))

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2021-03-15 19:12:00.328586 UTC