nLab supercommutative algebra

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Note: super algebra and supercommutative algebra both redirect for "super-commutative superalgebra".
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Context

Super-Algebra

Contents

Idea

A super-commutative algebra is a commutative algebra internal to the symmetric monoidal category of super vector spaces, hence a /2\mathbb{Z}/2-graded associative algebra such that for a,ba, b any two elements of homogeneous degree deg(a),deg(b)/2={0,1}deg(a), deg(b) \in \mathbb{Z}/2 = \{0,1\}, we have

ab=(1) deg(a)deg(b)ba. a \cdot b \;\;=\;\; (-1)^{deg(a) deg(b)} \; b \cdot a \,.

For more see at geometry of physics – superalgebra.

Examples

Last revised on February 16, 2023 at 07:27:08. See the history of this page for a list of all contributions to it.