nLab
Levi-Civita symbol

Contents

Contents

Idea

For nn \in \mathbb{N}, and σSym(n)\sigma \in Sym(n) a permutation of nn elements, the Levi-Civita symbol or antisymmetric symbol

ϵ σ(1),σ(2),,σ(n){±1} \epsilon_{\sigma(1), \sigma(2), \cdots, \sigma(n)} \;\in\; \{\pm 1\}

is (tensor-style notation for) the signature of the permutation.

Together with the Kronecker delta-notation, the Levi-Civita symbol is convenient in expressions subject to Einstein summation convention, then serving essentially as a combinatorial form of string diagram/Penrose notation in tensor categories.

References

See also

Last revised on March 16, 2020 at 13:53:25. See the history of this page for a list of all contributions to it.