Bulletin of the American Mathematical Society

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Book Information:

Author: J. M. G. Fell
Title: Induced representations and Banach $^*$-algebraic bundles
Additional book information: with an appendix due to A. Douady and L. Dal Soglio-Hérault, Lecture Notes in Math., vol. 582, Springer-Verlag, Berlin, Heidelberg, New York, 1977, 349 pp., $13.70.

1.

S. Albeverio and R. Høegh-Krohn, The energy representation of Sobolev-Lie groups (preprint).

Hyman Bass, Algebraic $K$-theory, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0249491

Robert C. Busby and Harvey A. Smith, Representations of twisted group algebras, Trans. Amer. Math. Soc. 149 (1970), 503–537. MR 264418, DOI 10.1090/S0002-9947-1970-0264418-8

4.

N. Dang Ngoc, Produits croisés restreints et extensions de groupes (preprint).

Platon C. Deliyannis, Holomorphic imprimitivities, Proc. Amer. Math. Soc. 16 (1965), 228–233. MR 176350, DOI 10.1090/S0002-9939-1965-0176350-2

Sergio Doplicher, Daniel Kastler, and Derek W. Robinson, Covariance algebras in field theory and statistical mechanics, Comm. Math. Phys. 3 (1966), 1–28. MR 205095

J. M. G. Fell, An extension of Mackey’s method to Banach $^{\ast }$ algebraic bundles, Memoirs of the American Mathematical Society, No. 90, American Mathematical Society, Providence, R.I., 1969. MR 0259619

8.

G. Frobenius, Über Relationen Zwischen den Charakteren einer Gruppe un denen ihrer Untergruppen, Sitzber. Preuss. Akad. Wiss. 1898, 501-515.

I. M. Gel′fand, M. I. Graev, and A. M. Veršik, Representations of the group of smooth mappings of a manifold $X$ into a compact Lie group, Compositio Math. 35 (1977), no. 3, 299–334. MR 578652

G. A. Goldin and D. H. Sharp, Lie algebras of local currents and their representations, Group Representations in Math. and Phys. (Battelle Seattle 1969 Rencontres), Lecture Notes in Phys., Vol. 6, Springer, Berlin, 1970, pp. 300–311. MR 0272325

Philip Green, The local structure of twisted covariance algebras, Acta Math. 140 (1978), no. 3-4, 191–250. MR 493349, DOI 10.1007/BF02392308

12.

A. Guichardet, Représentations de G, Seminaire Bourbaki 1975/76, no. 486.

D. G. Higman, Induced and produced modules, Canadian J. Math. 7 (1955), 490–508. MR 87671, DOI 10.4153/CJM-1955-052-4

R. S. Ismagilov, Unitary representations of the group of diffeomorphisms of the space $R^{n}$, $n\geq 2$, Funkcional. Anal. i Priložen. 9 (1975), no. 2, 71–72 (Russian). MR 0377974

A. A. Kirillov, Representations of certain infinite-dimensional Lie groups, Vestnik Moskov. Univ. Ser. I Mat. Meh. 29 (1974), no. 1, 75–83 (Russian, with English summary). Collection of articles dedicated to the memory of Ivan Georgievič Petrovskiĭ. (Russian). MR 0379762

Horst Leptin, Darstellung verallgemeinerter $L^{1}$-Algebren. II, Lectures on operator algebras (Tulane Univ. Ring and Operator Theory Year, 1970–1971, Vol. II; Dedicated to the memory of David M. Topping), Lecture Notes in Math., Vol. 247, Springer, Berlin, 1972, pp. 251–307 (German). MR 0370204

Ronald L. Lipsman, Group representations, Lecture Notes in Mathematics, Vol. 388, Springer-Verlag, Berlin-New York, 1974. A survey of some current topics. MR 0372116

George W. Mackey, Imprimitivity for representations of locally compact groups. I, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 537–545. MR 31489, DOI 10.1073/pnas.35.9.537

George W. Mackey, Induced representations of locally compact groups. I, Ann. of Math. (2) 55 (1952), 101–139. MR 44536, DOI 10.2307/1969423

George W. Mackey, Unitary representations of group extensions. I, Acta Math. 99 (1958), 265–311. MR 98328, DOI 10.1007/BF02392428

Kiiti Morita, Duality for modules and its applications to the theory of rings with minimum condition, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 6 (1958), 83–142. MR 96700

L. Pukanszky, Characters of connected Lie groups, Acta Math. 133 (1974), 81–137. MR 409728, DOI 10.1007/BF02392143

Marc A. Rieffel, Induced representations of $C^{\ast }$-algebras, Advances in Math. 13 (1974), 176–257. MR 353003, DOI 10.1016/0001-8708(74)90068-1

Marc A. Rieffel, Induced representations of rings, Canadian J. Math. 27 (1975), 261–270. MR 429996, DOI 10.4153/CJM-1975-032-0

1.

S. Albeverio and R. Høegh-Krohn, The energy representation of Sobolev-Lie groups (preprint).

2.

H. Bass, Algebraic K-theory, Benjamin, New York, 1968. MR 0249491

3.

R. C. Busby and H. A. Smith, Representations of twisted group algebras, Trans. Amer. Math. Soc. 149 (1970), 503-537. MR 264418

4.

N. Dang Ngoc, Produits croisés restreints et extensions de groupes (preprint).

5.

P. C. Deliyannis, Holomorphic imprimitivities, Proc. Amer. Math. Soc. 16 (1965), 228-233. MR 176350

6.

S. Doplicher, D. Kastler and D. Robinson, Covariance algebras in field theory and statistical mechanics, Comm. Math. Phys. 3 (1966), 1-28. MR 205095

7.

J. M. G. Fell, An extension of Mackey's method to Banach *-algebraic bundles, Mem. Amer. Math. Soc. No. 90 (1969). MR 259619

8.

G. Frobenius, Über Relationen Zwischen den Charakteren einer Gruppe un denen ihrer Untergruppen, Sitzber. Preuss. Akad. Wiss. 1898, 501-515.

9.

I. M. Gelfand, M. I. Graev and A. M. Versik, Representations of the group of smooth mapping of a manifold X into a compact Lie group, Compositio Math. 35 (1977), 299-334. MR 578652

10.

G. A. Goldin and D. H. Sharp, Lie algebras of local currents and their representations, Group Representations in Math. and Phys. (Battelle Seattle 1969 Rencontres), Lecture Notes in Physics, vol. 6, Springer, Berlin, 1970, pp. 300-311. MR 272325

11.

P. Green, The local structure of twisted covariance algebras (preprint). MR 493349

12.

A. Guichardet, Représentations de G, Seminaire Bourbaki 1975/76, no. 486.

13.

D. G. Higman, Induced and produced modules, Canad. J. Math. 7 (1955), 490-508. MR 87671

14.

R. C. Ismagilov, On the unitary representations of the group of diffeomorphisms of the space R, n ⩾ 2, Functional Anal. Appl. 9 (1975), 71-72. MR 377974

15.

A. A. Kirillov, Representations of some infinite-dimensional lie groups, Vestnik Moskov, Univ. Ser. I Mat. Meh. 29 (1974), 75-83. MR 379762

16.

H. Leptin, Darstellungen verallgemeinerter L¹-Algebren, II, Lectures on operator algebras, Vol. II, Lecture Notes in Math., vol 247, Springer-Verlag, Berlin and New York, 1972, pp. 251-307. MR 370204

17.

R. Lipsman, Group representations, Lecture Notes in Math., vol. 388, Springer-Verlag, Berlin and New York, 1974. MR 372116

18.

G. W. Mackey, Imprimitivity for representations of locally compact groups, I, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 537-545. MR 31489

19.

G. W. Mackey, Induced representations of locally compact groups. I, Ann. of Math. (2) 55 (1952), 101-139. MR 44536

20.

G. W. Mackey, Unitary representations of group extensions. I, Acta. Math. 99 (1958), 265-311. MR 98328

21.

K. Morita, Duality for modules and its applications to the theory of rings with minimum condition, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 6 (1958), 83-142. MR 96700

22.

L. Pukanszky, Characters of connected Lie groups, Acta Math. 133 (1974), 81-137. MR 409728

23.

M. A. Rieffel, Induced representations of C*-algebras, Advances in Math. 13 (1974), 176-257. MR 353003

24.

M. A. Rieffel, Induced representations of rings, Canad. J. Math. 27 (1975), 261-270. MR 429996