On Projective Unitary-Antiunitary Representations of Finite Groups
- 1 March 1972
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 13 (3) , 342-351
- https://doi.org/10.1063/1.1665982
Abstract
A generalization of Schur's treatment of projective representations is discussed for a very general class of representations occurring in physical theories: the projective representations by unitary and antiunitary operators. It is shown that for every finite group the projective unitary‐antiunitary (PUA) representations can be obtained from the ordinary unitary‐antiunitary representations of another finite group. The construction of such a representation group is treated. As an example we apply the theory for the determination of irreducible representations of subgroups of the Poincaré group. The classes of PUA representations for all finite crystallographic groups in spaces of dimension up to four are explicitly given.Keywords
This publication has 9 references indexed in Scilit:
- Electromagnetic compensating gauge transformationsPhysica, 1971
- Projective unitary antiunitary representations of locally compact groupsCommunications in Mathematical Physics, 1969
- Crystallographic groups in space and time: II. Central extensionsPhysica, 1969
- Magnetic Groups and Their CorepresentationsReviews of Modern Physics, 1968
- Ray representations of point groups and the irreducible representations of space groups and double space groupsPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1966
- Ray Representations of Finite Nonunitary GroupsJournal of Mathematical Physics, 1966
- On Unitary Ray Representations of Continuous GroupsAnnals of Mathematics, 1954
- Cohomology Theory in Abstract Groups. IAnnals of Mathematics, 1947
- Representations Induced in an Invariant SubgroupAnnals of Mathematics, 1937