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Supercommutative Algebra
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Geliefert zwischen Mo., 02.02.2026 und Di., 03.02.2026
Details
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a supercommutative algebra is a superalgebra (i.e. a Z2-graded algebra) such that for any two homogeneous elements x, y we have yx = (-1)^{ x y }xy., Equivalently, it is a superalgebra where the supercommutator [x,y] = xy - (-1)^{ x y }yx, always vanishes. Algebraic structures which supercommute in the above sense are sometimes referred to as skew-commutative associative algebras to emphasize the anti-commutation, or, to emphasize the grading, graded-commutative or, if the supercommutativity is understood, simply commutative. Any commutative algebra is a supercommutative algebra if given the trivial gradation (i.e. all elements are even). Grassmann algebras (also known as exterior algebras) are the most common examples of nontrivial supercommutative algebras. The supercenter of any superalgebra is the set of elements that supercommute with all elements, and is a supercommutative algebra. The even subalgebra of a supercommutative algebra is always a commutative algebra. That is, even elements always commute. Odd elements, on the other hand, always anticommute.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131236051
- Editor Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
- Größe H220mm x B220mm
- EAN 9786131236051
- Format Fachbuch
- Titel Supercommutative Algebra
- Herausgeber Betascript Publishing
- Anzahl Seiten 72
- Genre Mathematik
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