Defining the real Lie superalgebra as real Z2-graded vector space we classify real Manin supertriples and Drinfel’d superdoubles of superdimensions (2,2), (4,2), and (2,4). The Drinfel’d doubles of the superdimension (2,2) are then used for construction of the simplest σ-models related by Poisson–Lie T-plurality.

1.
D.
Leites
and
V.
Serganova
,
Teor. Mat. Fiz.
58
,
26
(
1984
).
3.
C.
Klimčík
and
P.
Ševera
,
Phys. Lett. B
351
,
455
(
1995
).
4.
R.
von Unge
,
J. High Energy Phys.
02
(
2002
)
014
.
5.
S. E.
Parkhomenko
,
JETP Lett.
64
,
877
(
1996
).
6.
7.
E.
Eghbali
and
A.
Rezaei-Aghdam
,
J. High Energy Phys.
09
(
2009
)
094
.
8.
C.
Juszczak
and
J. T.
Sobczyk
,
J. Math. Phys.
39
,
4982
(
1998
).
9.
X.
Gomez
,
J. Math. Phys.
41
,
4939
(
2000
).
10.
L.
Hlavatý
and
L.
Šnobl
,
Mod. Phys. Lett. A
17
,
429
(
2002
).
11.
L.
Šnobl
and
L.
Hlavatý
,
Int. J. Mod. Phys. A
17
,
4043
(
2002
).
12.
A.
Rogers
,
Supermanifolds, Theory and Applications
(
World Scientific
,
Singapore
,
2007
).
13.
N.
Backhouse
,
J. Math. Phys.
19
,
2400
(
1978
).
14.
By Am,n we denote the Abelian superalgebra of the superdimension (m,n).
15.
N.
Andruskiewitsch
,
Abh. Math. Semin. Univ. Hambg.
63
,
147
(
1993
).
16.
The other, rather exotic, possibilities were discussed in the bachelor thesis of Vysoký.
17.
G. I.
Olshanski
,
Lett. Math. Phys.
24
,
93
(
1992
).
18.
Differently from Ref. 13 we have denoted the superalgebra C1/21 as F because it differs from Cp=1/21.
You do not currently have access to this content.