Abstract
Abstract
A
Z
2
×
Z
2
-graded Lie superalgebra
g
is a
Z
2
×
Z
2
-graded algebra with a bracket
[
[
⋅
,
⋅
]
]
that satisfies certain graded versions of the symmetry and Jacobi identity. In particular, despite the common terminology,
g
is not a Lie superalgebra. We construct the most general orthosymplectic
Z
2
×
Z
2
-graded Lie superalgebra
o
s
p
(
2
m
1
+
1
,
2
m
2
|
2
n
1
,
2
n
2
)
in terms of defining matrices. A special case of this algebra appeared already in work of Tolstoy in 2014. Our construction is based on the notion of graded supertranspose for a
Z
2
×
Z
2
-graded matrix. Since the orthosymplectic Lie superalgebra
o
s
p
(
2
m
+
1
|
2
n
)
is closely related to the definition of parabosons, parafermions and mixed parastatistics, we investigate here the new parastatistics relations following from
o
s
p
(
2
m
1
+
1
,
2
m
2
|
2
n
1
,
2
n
2
)
. Some special cases are of particular interest, even when one is dealing with parabosons only.
Cited by
1 articles.
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