superalgebra
Look at other dictionaries:
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… … Wikipedia
Lie superalgebra — In mathematics, a Lie superalgebra is a generalisation of a Lie algebra to include a Z2 grading. Lie superalgebras are important in theoretical physics where they are used to describe the mathematics of supersymmetry. In most of these theories,… … Wikipedia
Representation of a Lie superalgebra — In the mathematical field of representation theory, a representation of a Lie superalgebra is an action of Lie superalgebra L on a Z2 graded vector space V , such that if A and B are any two pure elements of L and X and Y are any two pure… … Wikipedia
Poisson superalgebra — In mathematics, a Poisson superalgebra is a Z2 graded generalization of a Poisson algebra. Specifically, a Poisson superalgebra is an (associative) superalgebra A with a Lie superbracket: [cdot,cdot] : Aotimes A o Asuch that ( A , [ middot;,… … Wikipedia
Graded Lie algebra — In mathematics, a graded Lie algebra is a Lie algebra endowed with a gradation which is compatible with the Lie bracket. In other words, a graded Lie algebra is a Lie algebra which is also a nonassociative graded algebra under the bracket… … Wikipedia
Supermatrix — In mathematics and theoretical physics, a supermatrix is a Z2 graded analog of an ordinary matrix. Specifically, a supermatrix is a 2 times;2 block matrix with entries in a superalgebra (or superring). The most important examples are those with… … Wikipedia
Supersymmetry — In particle physics, supersymmetry (often abbreviated SUSY) is a symmetry that relates elementary particles of one spin to another particle that differs by half a unit of spin and are known as superpartners. In other words, in a supersymmetric… … Wikipedia
Supercommutative algebra — 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 Equivalently, it is a superalgebra where the supercommutator always vanishes. Algebraic structures… … Wikipedia
Supertrace — In the theory of superalgebras, if A is a commutative superalgebra, V is a free right A supermodule and T is an endomorphism from V to itself, then the supertrace of T , str( T ) is defined by the following tangle diagram::More concretely, if we… … Wikipedia
Super vector space — In mathematics, a super vector space is another name for a Z2 graded vector space, that is, a vector space over a field K with a given decomposition:V=V 0oplus V 1.The study of super vector spaces and their generalizations is sometimes called… … Wikipedia
