# nLab odd line

superalgebra

and

supergeometry

## Applications

The odd line is the supermanifold ${ℝ}^{0\mid 1}$ – a superpoint – characterized by the fact that its ${ℤ}_{2}$-graded algebra of functions is the algebra free on a single odd generator $\theta$: ${C}^{\infty }\left({ℝ}^{0\mid 1}\right)=ℝ\left[\theta \right]=ℝ\oplus \theta \cdot ℝ$.

This algebra is essentially the ring of dual numbers, but with the single generator in odd degree.

Revised on March 23, 2011 18:35:20 by Urs Schreiber (151.100.50.11)