A systematic study of locally operating multiplier realizations of nonconnected Lie groups of transformations is presented that generalizes previous results on connected groups. The semilinear locally operating multiplier realizations of a nonconnected group G are those obtained through an induction process from the finite‐dimensional semilinear representations of a given subgroup of a representation group Ḡ for G.

1.
H.
Hoogland
,
Nuovo Cimento B
32
,
427
(
1976
);
H.
Hoogland
,
J. Phys. A: Math. Gen.
11
,
797
,
1557
(
1978
).
2.
H. Hoogland, Ph.D. thesis, University of Nijmegen, 1977.
3.
V.
Bargman
,
Ann. Math.
59
,
1
(
1954
).
4.
E. P.
Wigner
,
Ann. Math.
40
,
149
(
1939
).
5.
J. F.
Cariñena
,
M. A.
del Olmo
, and
M.
Santander
,
Physica
114
,
420
(
1982
).
6.
M.
Asorey
,
J. F.
Cariñena
, and
M. A.
del Olmo
,
J. Phys. A: Math. Gen.
16
,
1603
(
1983
).
7.
J. F. Cariñena, M. A. del Olmo, and M. Santander, Lecture Notes in Physics, Vol. 201, edited by G. Denardo (Springer, Berlin, 1983).
8.
J. F.
Cariñena
,
M. A.
del Olmo
, and
M.
Santander
,
J. Phys. A: Math. Gen.
17
,
3091
(
1984
).
9.
J. F.
Cariñena
,
M. A.
del Olmo
, and
M.
Santander
,
J. Math. Phys.
26
,
2096
(
1985
).
10.
G. W.
Mackey
,
Ann. Math.
55
,
701
(
1952
)
[see also D. J. Simms, “Lie groups and quantum mechanics,” Lecture Notes in Physics, Vol. 52 (Springer, Berlin, 1969)].
11.
E. P. Wigner, “Unitary representations of the inhomogeneous Lorentz group including reflections,” in Group Theoretical Concepts and Methods in Elementary Particle Physics, edited by F. Gursey (Gordon and Breach, New York, 1964).
12.
U.
Cattaneo
,
J. Math. Phys.
19
,
452
(
1978
).
13.
J. F. Cariñena, and M. Santander, 20, 2168 (1979).
14.
R.
Shaw
and
J.
Lever
,
Commun. Math. Phys.
38
,
257
(
1974
).
15.
J. M. Levy‐Leblond, “Galilei Group and Galilei invariance,” in Group Theory and its Applications, edited by E. Loebl (Academic New York, 1971), Vol. II.
16.
J. F.
Cariñena
, and
M.
Santander
,
J. Math. Phys.
22
,
1548
(
1981
).
17.
J. G.
Dubois
,
Can. J. Phys.
51
,
1757
(
1973
).
18.
J. R.
Derome
and
J. G.
Dubois
,
Nuovo Cimento B
9
,
351
(
1972
).
19.
M. Valls, Tesina de Licenciatura, Universidad de Valladolid, 1977 (unpublished).
20.
H.
Bacry
,
Ph.
Combe
, and
J. L.
Richard
,
Nuovo Cimento A
67
,
267
(
1970
);
H.
Bacry
,
Ph.
Combe
, and
J. L.
Richard
,
70
,
289
(
1970
).,
Nuovo Cimento A
21.
Ph. Combe and J. L. Richard, Proceedings of the 2nd International Colloquium on Group Theoretical Methods in Physics, Vol. 2, edited by A. Janner and T. Jannsen (University of Nijmegen, Nijmegen, 1973).
22.
N.
Giovannini
,
Helv. Phys. Acta
50
,
337
,
349
(
1977
);
N.
Giovannini
,
Physica A
87
,
546
(
1977
).
23.
V.
Hussin
,
Nuovo Cimento A
65
,
39
(
1981
).
24.
J.
Beckers
, and
V.
Hussin
,
J. Math. Phys.
24
,
1286
,
1295
(
1983
).
25.
K. R. Parthasaraty, Multiplier on Locally Compact Groups, Lecture Notes in Physics, Vol. 93 (Springer, New York, 1969).
26.
P. M.
van den Broeck
,
J. Phys. A: Math. Gen.
9
,
855
(
1976
).
27.
M. Santander, Ph.D. thesis, University of Valladolid, 1977 (unpublished).
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