EXTENSION OF CHARACTERS ON THE NORMAL SUBGROUP OF A SEMI-DIRECT PRODUCT GROUP TO ONE-DIMENSIONAL PSEUDOREPRESENTATIONS OF THE GROUP
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초록
Investigations concerning the extension of characters on normal subgroups to one-dimensional pseudorepresentations of the enveloping groups are continued. The main result claims that, for a given (unitary) character f on a normal subgroup N of a given group G which is a semidirect product of N and some subgroup R ⊂ G, there is a one-to-one correspondence between the extensions of F to a one-dimensional pseudorepresentation of G and the one-dimensional pseudorepresentations of R.
Abstract
Investigations concerning the extension of characters on normal subgroups to one-dimensional pseudorepresentations of the enveloping groups are continued. The main result claims that, for a given (unitary) character f on a normal subgroup N of a given group G which is a semidirect product of N and some subgroup R ⊂ G, there is a one-to-one correspondence between the extensions of F to a one-dimensional pseudorepresentation of G and the one-dimensional pseudorepresentations of R.
참고문헌 (7)
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- A. I. Shtern, "EXTENSION OF PSEUDOCHARACTERS FROM NORMAL SUBGROUPS, II", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 19(2), pp.213~218 (2016), 장전수학회
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- A. I. Shtern, "Quasisymmetry. II", Russ. J. Math. Phys, 14(3), pp.332~356 (2007)
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- A. I. Shtern, "Specific Properties of One-Dimensional Pseudorepresentations of Groups", Fundam. Prikl. Matem, 20(6) (2015)
- A. I. Shtern, "Continuous one-dimensional pseudorepresentations of almost connected locally compact groups", Advanced Studies in Contemporary Mathematics, 26(3), pp.541~546 (2016), 장전수학회