- 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...
- In mathematics, a Lie
superalgebra is a
generalisation of a Lie
algebra to
include a Z2‑grading. Lie
superalgebras are
important in
theoretical physics...
-
Poisson superalgebra is a Z2-graded
generalization of a
Poisson algebra. Specifically, a
Poisson superalgebra is an (****ociative)
superalgebra A with a...
- 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...
- In mathematics, a
supercommutative (****ociative)
algebra is a
superalgebra (i.e. a Z2-graded algebra) such that for any two
homogeneous elements x, y we...
- then V is
called a
vertex operator superalgebra. One of the
simplest examples is the
vertex operator superalgebra generated by a
single free
fermion ψ...
-
supergraded Lie
superalgebra is a
further generalization of this
notion to the
category of
superalgebras in
which a
graded Lie
superalgebra is
endowed with...
-
Victor G (1977), "classification of
simple Z-graded Lie
superalgebras and
simple Jordan superalgebras",
Communications in Algebra, 5 (13): 1375–1400, doi:10...
-
interesting examples. It is also
possible to
extend the
definition to
superalgebras. A
generalized Kac–Moody
algebra can be
graded by
giving ei
degree 1...
-
purely algebraically as the
universal enveloping algebra of the Lie
superalgebra. In a
similar way one can
define an
affine algebraic supergroup as a...
