# superalgebra

A graded algebra^{} $A$ is said to be a superalgebra if it has a $\mathbb{Z}/2\mathbb{Z}$ grading.
As a vector space^{}, a superalgebra has a decomposition into two homogeneous^{} subspaces^{}, $A={A}_{0}\oplus {A}_{1}$.
The homogeneous subspace ${A}_{0}$ is known as the space of even elements of $A$, and ${A}_{1}$ is known as the space of odd elements.
Let $|a|$ denote the degree of a homogeneous element^{}.
That is, $|a|=0$ if $a\in {A}_{0}$ and $|a|=1$ if $a\in {A}_{1}$.
The degree satisfies $|ab|=|a|+|b|$.

Title | superalgebra |

Canonical name | Superalgebra |

Date of creation | 2013-03-22 12:46:18 |

Last modified on | 2013-03-22 12:46:18 |

Owner | mhale (572) |

Last modified by | mhale (572) |

Numerical id | 7 |

Author | mhale (572) |

Entry type | Definition |

Classification | msc 16W55 |

Synonym | super algebra |

Related topic | Supernumber |

Related topic | Supercommutative |

Related topic | LieSuperalgebra |

Related topic | LieSuperalgebra3 |

Related topic | GradedAlgebra |