Super linear algebra | Algebras

Superalgebra

In mathematics and theoretical physics, a superalgebra is a Z2-graded algebra. That is, it is an algebra over a commutative ring or field with a decomposition into "even" and "odd" pieces and a multiplication operator that respects the grading. The prefix super- comes from the theory of supersymmetry in theoretical physics. Superalgebras and their representations, supermodules, provide an algebraic framework for formulating supersymmetry. The study of such objects is sometimes called super linear algebra. Superalgebras also play an important role in related field of supergeometry where they enter into the definitions of graded manifolds, supermanifolds and . (Wikipedia).

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Related pages

Clifford algebra | Supermanifold | Super vector space | Supercommutative algebra | Supersymmetry | Supergeometry | Torsion (algebra) | Subalgebra | Direct sum of modules | Automorphism | Identity element | Monoid (category theory) | Bilinear map | Bimodule | Polynomial ring | Algebra (ring theory) | Graded manifold | Tensor algebra | Characteristic (algebra) | Mathematics | Field (mathematics) | Integer | Tensor product of algebras | Involution (mathematics) | Lie algebra | Category theory | Exterior algebra | Category (mathematics) | Bilinear form | Graded ring | Monoidal category | Lie superalgebra | Universal enveloping algebra | Supermodule | Endomorphism | Modular arithmetic | Module (mathematics) | Commutative ring