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Draft:Eberhard Kirchberg

  • Comment: Reasons for the previous decline have not been addressed. Turnagra (talk) 17:36, 29 November 2023 (UTC)
  • Comment: The vast majority of citations are to primary sources. 97198 (talk) 13:24, 1 July 2023 (UTC)
Eberhard Kirchberg
Born14 January 1946
Died12 August 2022
Alma materUniversity of Greifswald
Scientific career
FieldsMathematics, Functional Analysis, Operator Algebras, C*-algebras, von Neumann Algebras
InstitutionsHeidelberg University
Thesis Hopf-W*-Algebren und nicht-kommutative Dualitätstheorie  (1978)

Eberhard Kirchberg (14 January 1946 -- 12 August 2022) was a German mathematician and Professor of Functional Analysis at Humboldt University in Berlin specializing in operator algebras, K-theory, and noncommutative geometry. He made fundamental contributions to the study of operator algebras and is best known for his work on the structure and classification of C*-algebras. Throughout his career Kirchberg undertook a remarkably extensive study of exactness of C*-algebras whose applications have influenced many branches of analysis.[1]

Life and work edit

Kirchberg grew up in the town of Freiberg in the former country of East Germany. He earned his Ph.D. in mathematics from the University of Greifswald in 1978,[2] and afterward worked as a scientific assistant at the Institute of Mathematics of the Academy of Sciences in East Berlin.

Kirchberg had a reputation as a political dissident who was critical East German policy.[3] In 1988 he participated in a demonstration organized by a Protestant church, after which he was arrested and given the choice of prison or deportation to West Germany. Kirchberg chose deportation, and after relocating to West Germany he obtained a job as a Wissenschaftlicher Assistent under the supervision of Joachim Cuntz at Heidelberg University. While at Heidelberg Kirchberg produced an influential series of papers that were published in journals such as Inventiones Mathematicae, [4] Crelle's Journal,[5] and Mathematische Annalen.[6] Some of Kirchberg's most important contributions during this time were unexpected reformulations of the Connes embedding problem, including Kirchberg's QWEP conjecture, which asks whether every C*-algebra is a quotient of a C*-algebras with the weak expectation property. In his work Kirchberg also initiated the study of exactness of C*-algebras, an analytic property related to tensor products of C*-algebras, which has played an important role in the study of C*-algebras as well as in group theory.

In 1993, when the East German universities were restructured following the German reunification, Kirchberg was given a Professorship at the Humboldt University in Berlin. In 1994, Kirchberg was an invited speaker at the International Congress of Mathematicians in Zurich, [7] where he announced several important theorem on the structure of C*-algebras. This was a starting point for important work in the classification of C*-algebras, and eventually led to the Kirchberg-Phillips classification theorem, which states that certain simple and purely infinite C*-algebras (now known as Kirchberg algebras) are classified by the pair of their K-groups (i.e., the K0-group and K1-group provided by K-theory). [8] This theorem, together with Elliott's Classification Theorem for AF-algebras, laid the foundation for deep work by many experts in operator algebras that ultimately produced a classification theorem for a more general class of simple C*-algebras in terms of K-theory.[9] This classification of certain simple C*-algebras is widely regarded as one of the most important results in operator algebras.[10] [11]

In the last years of his life, Kirchberg avoided the spotlight but continued to work on refinements and extensions of his results. He passed away on August 12, 2022.[3]

References edit

  1. ^ Anantharaman-Delaroche, Claire, Amenability, exactness and weak containment property for groupoids, arXiv preprint, https://arxiv.org/abs/2306.17613
  2. ^ Math Genealogy, entry for Eberhard Kirchberg
  3. ^ a b Online Obituary for Eberhard Kirchberg at Humboldt University (PDF)
  4. ^ Kirchberg, Eberhard, On nonsemisplit extensions, tensor products and exactness of group C*-algebras. Invent Math 112, 449--489 (1993). DOI 10.1007/BF01232444
  5. ^ Kirchberg, Eberhard, Commutants of unitaries in UHF algebras and functorial properties of exactness. J. Reine Angew. Math. 452, 39--77 (1994). DOI 10.1515/crll.1994.452.39
  6. ^ Kirchberg, Eberhard, Discrete groups with Kazhdan's property T and factorization property are residually finite. Math. Ann. 299, 551–563 (1994). DOI 10.1007/BF01459798
  7. ^ International Congress of Mathematicians, Speaker List, [1]
  8. ^ Rørdam, M. Classification of nuclear, simple C∗-algebras. Classification of nuclear C∗-algebras. Entropy in operator algebras, 1–145, Encyclopaedia Math. Sci., 126, Oper. Alg. Non-commut. Geom., 7, Springer, Berlin, 2002. DOI 10.1007/978-3-662-04825-2_1
  9. ^ Tikuisis, Aaron; White, Stuart; Winter, Wilhelm Quasidiagonality of nuclear C*-algebras. Ann. of Math. (2) 185, no. 1, 229–284 (2017). DOI 2017.185.1.4
  10. ^ Winter, Wilhelm Structure of nuclear C*-algebras: from quasidiagonality to classification and back again. Proceedings of the International Congress of Mathematicians --- Rio de Janeiro 2018. Vol. III. Invited lectures, 1801–1823, World Sci. Publ., Hackensack, NJ, 2018.
  11. ^ Elliott, George A.; Toms, Andrew S. Regularity properties in the classification program for separable amenable C∗-algebras. Bull. Amer. Math. Soc. (N.S.) 45, no. 2, 229--245 (2008). DOI 10.1090/S0273-0979-08-01199-3

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