Fungrim symbol: SL2Z

Symbol: SL2Z —

\operatorname{SL}_2(\mathbb{Z})

— Modular group

Whether

\operatorname{SL}_2(\mathbb{Z})

\operatorname{PSL}_2(\mathbb{Z})

should be called "the modular group" is an arbitrary convention. Here we allow any element of

\operatorname{SL}_2(\mathbb{Z})

to represent an element of the modular group, but we use

\operatorname{PSL}_2(\mathbb{Z})

when uniqueness is desired.

Definitions:

Fungrim symbol	Notation	Short description
`SL2Z`	$\operatorname{SL}_2(\mathbb{Z})$	Modular group
`PSL2Z`	$\operatorname{PSL}_2(\mathbb{Z})$	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."))

Topics using this symbol

The symbol SL2Z appears in 3 topics:

Modular transformations (in 6 entries)
Modular j-invariant (in 1 entries)
Dedekind eta function (in 1 entries)

Entries using this symbol

The symbol SL2Z appears in 8 entries: