Supergroup (Physics)
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High Quality Content by WIKIPEDIA articles! The concept of supergroup is a generalization of that of group. In other words, every group is a supergroup but not every supergroup is a group. First, let us define a Hopf superalgebra. A Hopf algebra can be defined category-theoretically as an object in the category of vector spaces together with a collection of morphisms (?, ?, ?, ?, S) satisfying certain commutativity axioms. A Hopf superalgebra can be defined in a completely analogous manner in the category of super vector spaces. The amounts to the additional requirement that the morphisms ?,…mehr

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High Quality Content by WIKIPEDIA articles! The concept of supergroup is a generalization of that of group. In other words, every group is a supergroup but not every supergroup is a group. First, let us define a Hopf superalgebra. A Hopf algebra can be defined category-theoretically as an object in the category of vector spaces together with a collection of morphisms (?, ?, ?, ?, S) satisfying certain commutativity axioms. A Hopf superalgebra can be defined in a completely analogous manner in the category of super vector spaces. The amounts to the additional requirement that the morphisms ?, ?, ?, ?, S are all even. There are many possible supergroups. The ones of most interest in theoretical physics are the ones which extend the Poincaré group or the conformal group. In this setup, one is particularly interested with the orthosymplectic groups Osp(N/M) and the superconformal groups SU(N/M).