1,502 research outputs found
generalizations of superconformal Galilei algebras and their representations
We introduce two classes of novel color superalgebras of grading. This is done by realizing members of each in the
universal enveloping algebra of the supersymmetric extension of
the conformal Galilei algebra. This allows us to upgrade any representation of
the super conformal Galilei algebras to a representation of the graded algebra. As an example, boson-fermion Fock space
representation of one class is given. We also provide a vector field
realization of members of the other class by using a generalization of the
Grassmann calculus to graded setting.Comment: 17 pages, no figur
Maps and twists relating and the nonstandard : unified construction
A general construction is given for a class of invertible maps between the
classical and the Jordanian algebras. Different maps
are directly useful in different contexts. Similarity trasformations connecting
them, in so far as they can be explicitly constructed, enable us to translate
results obtained in terms of one to the other cases. Here the role of the maps
is studied in the context of construction of twist operators between the
cocommutative and noncocommutative coproducts of the and
algebras respectively. It is shown that a particular map called
the `minimal twist map' implements the simplest twist given directly by the
factorized form of the -matrix of Ballesteros-Herranz. For other
maps the twist has an additional factor obtainable in terms of the similarity
transformation relating the map in question to the minimal one. The series in
powers of for the operator performing this transformation may be obtained
up to some desired order, relatively easily. An explicit example is given for
one particularly interesting case. Similarly the classical and the Jordanian
antipode maps may be interrelated by a similarity transformation. For the
`minimal twist map' the transforming operator is determined in a closed form.Comment: LaTeX, 13 page
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