Geodesic
Compact Induced Representations
Canadian journal of mathematics, Tome 24 (1972) no. 1, pp. 5-16

Voir la notice de l'article provenant de la source Cambridge University Press

In [15; 16; 17], Horst Leptin introduced what he called generalized group algebras. These Banach *-algebras are formed by letting a locally compact group G act on a Banach *-algebra A both by *-automorphisms and by a cocycle with values in the multiplier algebra, M (A ), of A. We will review the precise construction later, but for now we remark that examples include the group algebra of a group extension, the covariance algebras of quantum field theory, the “projective group algebras” of a group G (that is, for each complex-valued cocycle λ, called a multiplier in the literature, the Banach *-algebra whose nondegenerate *-representations are in bijective correspondence with the λ-projective representations of G), and the twisted group algebras of Edwards and Lewis [8; 9]. 
Busby, Robert C.; Schochetman, Irwin. Compact Induced Representations. Canadian journal of mathematics, Tome 24 (1972) no. 1, pp. 5-16. doi: 10.4153/CJM-1972-002-3
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[1] 1. Bourbaki, N., Topologie general, 4th edition (Hermann, Paris, 1965). Google Scholar

[2] 2. Busby, R. C., Double centralizers and extensions of C*-algebras, Trans. Amer. Math. Soc. 132 (1968), 79–99. Google Scholar

[3] 3. Busby, R. C., On a theorem of Fell (to appear in Proc. Amer. Math. Soc.). Google Scholar

[4] 4. Busby, R. C. and Smith, H. A., Representations of twisted group algebras, Trans. Amer. Math. Soc. 149 (1970), 503–537. Google Scholar

[5] 5. Busby, R. C., Schochetman, I., and Smith, H. A., Integral operators and the compactness of induced representations (to appear in Trans. Amer. Math. Soc). Google Scholar

[6] 6. Dixmier, J., Les C*-algèbres et leurs représentations, Cahiers Scientifiques, fasc. 29 (Gauthier-Villars, Paris, 1964). Google Scholar

[7] 7. Dixmier, J., Les algèbres d'opérateurs dans l'espace Hilbertien, Cahiers Scientifiques, fasc. 25 (Gauthier-Villars, Paris, 1957). Google Scholar

[8] 8. Edwards, C. M. and Lewis, J. T., Twisted group algebras. I, Comm. Math. Phys. 13 (1969), 119–130. Google Scholar

[9] 9. Edwards, C. M. and Lewis, J. T., Twisted group algebras. II, Comm. Math. Phys. 13 (1969), 131–141. Google Scholar

[10] 10. Fell, J. M. G., Weak containment and induced representations of groups, Can. J. Math. 14 (1962), 237–268. Google Scholar

[11] 11. Fell, J. M. G., Weak containment and induced representations of groups. II, Trans. Amer. Math. Soc. 110 (1964), 424–447. Google Scholar

[12] 12. Glimm, J., Locally compact transformation groups, Trans. Amer. Math. Soc. 101 (1961), 124–138. Google Scholar

[13] 13. Glimm, J., Type I C*-algebras, Ann. of Math. 73 (1961), 572–612. Google Scholar

[14] 14. Johnson, B. E., An introduction to the theory of double centralizers, Proc. London Math. Soc. 14 (1964), 411–429. Google Scholar

[15] 15. Leptin, H., Verallgemeinerte L1-Algebren, Math. Ann. 159 (1965), 51–76. Google Scholar

[16] 16. Leptin, H., Verallgemeinerte L1-Algebren und projektive Darstellungen lokal kompakter Gruppen. I, Invent. Math. 8 (1967), 257–281. Google Scholar

[17] 17. Leptin, H., Verallgemeinerte L1-Algebren und projektive Darstellungen lokal kompakter Gruppen. II, Invent. Math. 4 (1967), 68–86. Google Scholar

[18] 18. Mackey, G., Borel structures in groups and their duals, Trans. Amer. Math. Soc. 85 (1957), 134–165. Google Scholar

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