TeXipedia

mathfrak

Renders text in a decorative Fraktur font style, commonly used for special mathematical sets and algebraic structures.

Overview

Provides an ornate, gothic-style mathematical font particularly valued in advanced mathematics for denoting specific mathematical objects and structures.

  • Traditionally used to represent Lie algebras and other algebraic structures
  • Common in abstract algebra for denoting ideals or special number systems
  • Helps distinguish special sets like the real numbers (\mathfrak{R}) from standard notation
  • Particularly prevalent in German mathematical literature and classical mathematical texts
  • Offers visual distinction when multiple font styles are needed in complex mathematical notation

Examples

Defining a Lie algebra using Fraktur font

g=sl(2,R)\mathfrak{g} = \mathfrak{sl}(2,\mathbb{R}) 
\mathfrak{g} = \mathfrak{sl}(2,\mathbb{R})

Denoting a mathematical ring using Fraktur notation

p⊂R\mathfrak{p} \subset \mathfrak{R} 
\mathfrak{p} \subset \mathfrak{R}

Representing ideals in algebraic number theory

a=⟨2,1+−5⟩\mathfrak{a} = \langle 2, 1 + \sqrt{-5} \rangle 
\mathfrak{a} = \langle 2, 1 + \sqrt{-5} \rangle