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In theoretical physics, a super-Poincaré algebra is an extension of the Poincaré algebra to incorporate supersymmetry, a relation between bosons and fermions. They are examples of supersymmetry algebras (without central charges or internal symmetries), and are Lie superalgebras. Thus a super-Poincaré algebra is a Z2-graded vector space with a graded Lie bracket such that the even part is a Lie algebra containing the Poincaré algebra, and the odd part is built from spinors on which there is an anticommutation relation with values in the even part.

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  • In theoretical physics, a super-Poincaré algebra is an extension of the Poincaré algebra to incorporate supersymmetry, a relation between bosons and fermions. They are examples of supersymmetry algebras (without central charges or internal symmetries), and are Lie superalgebras. Thus a super-Poincaré algebra is a Z2-graded vector space with a graded Lie bracket such that the even part is a Lie algebra containing the Poincaré algebra, and the odd part is built from spinors on which there is an anticommutation relation with values in the even part. (en)
  • In fisica teorica, la superalgebra di Poincaré (o algebra di super-Poincaré) estende l'algebra di Poincaré con l'aggiunta della supersimmetria, una relazione tra bosoni e fermioni. La più semplice estensione supersimmetrica dell'algebra di Poincaré contiene due spinori di Weyl che soddisfano alla seguente relazione di anti-commutazione: e tutte le relazioni di anti-commutatione fra le e le sono nulle. Dove i sono i generatori delle traslazioni, le sono le matrici di Pauli e le sono le supercariche ovvero sono i generatori di una trasformazione di supersimmetria. (it)
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  • In theoretical physics, a super-Poincaré algebra is an extension of the Poincaré algebra to incorporate supersymmetry, a relation between bosons and fermions. They are examples of supersymmetry algebras (without central charges or internal symmetries), and are Lie superalgebras. Thus a super-Poincaré algebra is a Z2-graded vector space with a graded Lie bracket such that the even part is a Lie algebra containing the Poincaré algebra, and the odd part is built from spinors on which there is an anticommutation relation with values in the even part. (en)
  • In fisica teorica, la superalgebra di Poincaré (o algebra di super-Poincaré) estende l'algebra di Poincaré con l'aggiunta della supersimmetria, una relazione tra bosoni e fermioni. La più semplice estensione supersimmetrica dell'algebra di Poincaré contiene due spinori di Weyl che soddisfano alla seguente relazione di anti-commutazione: e tutte le relazioni di anti-commutatione fra le e le sono nulle. Dove i sono i generatori delle traslazioni, le sono le matrici di Pauli e le sono le supercariche ovvero sono i generatori di una trasformazione di supersimmetria. (it)
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  • Superalgebra di Poincaré (it)
  • Super-Poincaré algebra (en)
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