×
Morris, Sidney A.

Karl Heinrich Hofmann and the structure of compact groups and pro-Lie groups. (English) Zbl 1526.22001

J. Lie Theory 33, No. 1, 5-28 (2023).
Summary: This article is dedicated to Karl Heinrich Hofmann on his 90th birthday. The first part of the article records some biographical facts about him. The second part focuses on the research papers and books he published with the author of this article over the last 45 years. These results concern the structure of compact groups and pro-Lie groups.

Cited in 1 Document

MSC:

22-03 History of topological groups
01A70 Biographies, obituaries, personalia, bibliographies
22C05 Compact groups
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties

Keywords:

topological group; Lie group; compact group; pro-Lie group; Lie algebra; duality; Pontryagin duality; LCA group

Biographic References:

Hofmann, Karl Heinrich
Cite Review PDF
Full Text: Link

References:

[1] M. Aigner, G. M. Ziegler: Proofs from The Book, with illustrations by K. H. Hofmann, Springer, Berlin (2018). · Zbl 1392.00001
[2] C. Bessaga, A. Pelczyński: Selected Topics in Infinite Dimensional Topology, Mathe-matical Monographs 58, Polish Scientific Publishers, Warsaw (1975). · Zbl 0304.57001
[3] R. Brown, P. J. Higgins, S. A. Morris: Countable products and sums of lines and cir-cles: their closed subgroups, quotients and duality properties, Math. Proc. Cambridge Phil. Soc. 78 (1975) 19-32. · Zbl 0304.22001
[4] E.Cech: On bicompact spaces, Annals of Mathematics 38/4 (1937) 823-844. · JFM 63.0570.02
[5] T. P. Chalebgwa, S. A. Morris: A continuous homomorphism of a thin set onto a fat set, Bull. Australian Math. Soc. 106/3 (2022) 500-503. · Zbl 1503.54008
[6] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove, D. S. Scott: Con-tinuous Lattices and Domains, Cambridge University Press, Cambridge (2003). · Zbl 1088.06001
[7] H. Glöckner, K.-H. Neeb: Infinite Dimensional Lie Groups: General Theory and Main Examples, Graduate Texts in Mathematics 935, Springer, New York (2015).
[8] M. I. Graev: Free topological groups (Russian), Izv. Akad. Nauk SSSR, Ser. Mat. 12 (1948) 279-321. English translation in Amer. Math. Soc. Translations 35 (1951). Reprinted in Amer. Math. Soc. Translations (l) 8 (1962) 305-364.
[9] W. Herfort, K. H. Hofmann, F. G. Russo: Periodic Locally Compact Groups, Studies in Mathematics 71, De Gruyter, Berlin (2019). · Zbl 1423.22001
[10] K. H. Hofmann: Introduction to the Theory of Compact Groups I, Tulane University, New Orleans (1966-67).
[11] K. H. Hofmann: Introduction to the Theory of Compact Groups II, Tulane University, New Orleans (1968-69).
[12] K. H. Hofmann: Arc components in locally compact groups are Borel sets, Bull. Aus-tral. Math. Soc. 65 (2002) 1-8. · Zbl 1009.22006
[13] K. H. Hofmann, S. A. Morris: Locally compact products and coproducts in categories of topological groups, Bull. Austral. Math. Soc. 17 (1977) 401-417. · Zbl 0365.22006
[14] K. H. Hofmann, S. A. Morris: Free compact groups. I: Free compact abelian groups, Topology Appl. 23 (1986) 101-102. · Zbl 0627.22004
[15] K. H. Hofmann, S. A. Morris: Free compact groups. II: The center, Topology Appl. 28 (1988) 215-231. · Zbl 0638.22002
[16] K. H. Hofmann, S. A. Morris: Free compact groups. III: Free semisimple compact groups, in: Categorical Topology and its Applications to Analysis, J. Adamek et al. (eds.), World Scientific Publishers, Singapore (1989) 208-219.
[17] K. H. Hofmann, S. A. Morris: Weight and c, J. Pure Applied Algebra 68 (1990) 181-194. · Zbl 0728.22006
[18] K. H. Hofmann, S. A. Morris: The Lie Theory of Connected Pro-Lie Groups: A Struc-ture Theory for Pro-Lie Algebras, and Connected Locally Compact Groups, European Mathematical Society, Zurich (2007); 2nd ed.: The Structure of Pro-Lie Groups, Eu-ropean Mathematical Society, Zurich (2023). · Zbl 1153.22006
[19] K. H. Hofmann, S. A. Morris: Contributions to the structure of connected pro-Lie groups, Topology Proc. 33 (2009) 225-237. · Zbl 1221.22001
[20] K. H. Hofmann, S. A. Morris: The structure of almost connected pro-Lie groups, J. Lie Theory 21 (2011) 347-383. · Zbl 1226.22002
[21] K. H. Hofmann, S. A. Morris: Pro-Lie groups: a survey with open problems, Axioms 4 (2015) 294-312. · Zbl 1415.22005
[22] K. H. Hofmann, S. A. Morris: The Structure of Compact Groups: A Primer for the Student -A Handbook for the Expert, 4th ed., De Gruyter, Berlin (2020). · Zbl 1441.22001
[23] Morris
[24] K. H. Hofmann, S. A. Morris: Advances in the theory of compact groups and pro-Lie groups in the last quarter century, Axioms 10 (2021) 190.
[25] K. H. Hofmann, P. S. Mostert: Elements of Compact Semigroups, C. E. Merrill Books, Columbus (1966). · Zbl 0161.01901
[26] K. H. Hofmann, K.-H. Neeb: Pro-Lie groups as infinite dimensional Lie groups, Math. Proc. Cambridge Phil. Soc. 146 (2008) 351-378. · Zbl 1165.22017
[27] S. Kakutani: Free topological groups and infinite direct product topological groups, Proc. Imp. Acad. Tokyo 20 (1944) 595-598. · Zbl 0063.03105
[28] S. Maclane: Categories for the Working Mathematician, Springer, New York (1971). · Zbl 0232.18001
[29] A. A. Markov: On free topological groups (Russian), C. R. (Doklady) Acad. Sci. URSS, (N.S.) 31 (1941) 299-301. Izv. Akad. Nauk SSSR, Ser. Math. 9 (1945), 3-64. English translation in Amer. Math. Soc. Translations 30 (1950) 11-88; reprinted in Amer. Math. Soc. Translations (l) 8 (1962) 195-273.
[30] D. Montgomery, L. Zippin: Topological Transformation Groups, Interscience Pub-lisher, New York (1955). · Zbl 0068.01904
[31] S. A. Morris: Varieties of topological groups, Bull. Austral. Math. Soc. 1 (1969) 145-160. · Zbl 0172.31404
[32] S. A. Morris: Free compact abelian group, Mat. Cas. Slov. Akad. Vied 22 (1972) 141-147. · Zbl 0235.22012
[33] S. A. Morris: Pontryagin Duality and the Structure of Locally Compact Abelian Groups, Cambridge University Press, Cambridge (1977). · Zbl 0446.22006
[34] S. A. Morris: Duality and structure of locally compact abelian groups ... for the lay-man, Math. Chronicle 8 (1979) 39-56. · Zbl 0452.22004
[35] J. Nielsen: Die Isomorphismen der allgemeinen unendlichen Gruppe mit zwei Erzeu-genden, Math. Annalen. 78 (1917) 385-397. · JFM 46.0175.01
[36] J. C. Oxtoby: Cartesian products of Baire spaces, Fundamenta Math. 49 (1961) 157-166. · Zbl 0113.16402
[37] S. Shelah: Infinite abelian groups, Whitehead problem, and some constructions, Israel J. Math. 18 (1974) 243-256. · Zbl 0318.02053
[38] S. Shelah: The consistency of Ext(G, Z), Israel J. Math. 39 (1981) 74-82. · Zbl 0464.20043
[39] M. H. Stone: Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937) 375-481. · JFM 63.1173.01
[40] A. Tychonoff: Über die topologische Erweiterung von Räumen, Math. Annalen 102 (1930) 544-561. · JFM 55.0963.01
[41] W. von Dyck: Gruppentheoretische Studien, Math. Annalen 20 (1882) 1-44.
[42] J. S. Wilson: Profinite Groups, Oxford University Press, Oxford (1998). · Zbl 0909.20001
[43] H. Yamabe: On the conjecture of Iwasawa and Gleason, Ann. of Math. (2) 58 (1953) 48-54. · Zbl 0053.01601
[44] H. Yamabe: Generalization of a theorem of Gleason, Ann. of Math. (2) 58 (1953) 351-365. · Zbl 0053.01602
[45] Sidney A. Morris, (1) School of Engineering, IT and Physical Sciences, Federation University, Ballarat, Victoria, Australia; (2) Department of Mathematical and Physical Sciences, La Trobe University, Melbourne, Victoria, Australia;
[46] Morris.Sidney@gmail.com, ORCID: 0000-0002-0361-576X.
[47] Received September 21, 2022 and in final form September 30, 2022
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.