DOI QR코드

DOI QR Code

EXTENDING REPRESENTATIONS OF H TO G WITH DISCRETE G/H

  • CHO JIN-HWAN (Department of Mathematics The University of Suwon) ;
  • MASUDA MIKIYA (Department of Mathematics Osaka City University) ;
  • SUH DONG YOUP (Department of Mathematics Korea Advanced Institute of Science and Tehcnology)
  • Published : 2006.01.01

Abstract

The article deals with the problem of extending representations of a closed normal subgroup H to a topological group G. We show that the standard technique using group cohomology to solve the problem in the case of finite groups can be generalized in the category of topological groups if G/H is discrete.

References

  1. D. J. Benson, Representations and cohomology. I. Basic representation theory of finite groups and associative algebras, Cambridge Studies in Advanced Mathematics, 30. Cambridge University Press, Cambridge, 1991
  2. T. Brocker and T. tom Dieck, Representations of compact Lie groups, Graduate Texts in Mathematics, 98. Springer-Verlag, New York, 1985
  3. K. S. Brown, Cohomology of groups, Graduate Texts in Mathematics, 87. Springer-Verlag, New York-Berlin, 1982
  4. J. -H. Cho, S. S. Kim, M. Masuda, and D. Y. Suh, Classification of equivariant complex vector bundles over a circle, J. Math. Kyoto Univ. 41 (2001), no. 3, 517-534 https://doi.org/10.1215/kjm/1250517616
  5. J. -H. Cho, S. S. Kim, M. Masuda, and D. Y. Suh, Classification of equivariant real vector bundles over a circle, J. Math. Kyoto Univ. 42 (2002), no. 2, 223-242 https://doi.org/10.1215/kjm/1250283867
  6. J. -H. Cho, M. K. Kim, and D. Y. Suh, On extensions of representations for compact Lie groups, J. Pure Appl. Algebra, 178 (2003), no. 3, 245-254 https://doi.org/10.1016/S0022-4049(02)00212-8
  7. A. H. Clifford, Representations induced in an invariant subgroup, Ann. of Math.(2) 38 (1937), no. 3, 533-550 https://doi.org/10.2307/1968599
  8. K. H. Hofmann and S. A. Morris, The structure of compact groups, A primer for the student-a handbook for the expert. de Gruyter Studies in Mathematics, 25. Walter de Gruyter & Co., Berlin, 1998
  9. I. M. Isaacs, Character theory of finite groups, Pure and Applied Mathematics, No. 69. Academic Press, New York-London, 1976
  10. I. M. Isaacs, Extensions of group representations over arbitrary fields, J. Algebra 68 (1981), no. 1, 54-74 https://doi.org/10.1016/0021-8693(81)90284-2
  11. L. S. Pontryagin, Topological groups, Translated from the second Russian edition by Arlen Brown Gordon and Breach Science Publishers, Inc., New York-London-Paris, 1966