Projects in Mathematics Muenster

Research area B: Spaces and Operators
Unit B3: Operator algebras & mathematical physics

Further Projects
CRC 1442: Geometry: Deformation and Rigidity - D02: Exotic crossed products and the Baum–Connes conjecture The Baum–Connes conjecture on the K-theory of crossed products by group actions on C*-algebras is one of the central problems in noncommutative geometry. The conjecture holds for large classes of groups and has important applications in other areas of mathematics. However, there are groups for which the conjecture fails to be true and in this project we study a new formulation of the conjecture due to Baum, Guentner and Willett which avoids the known counterexamples for the classical one. This involves new exotic crossed product functors which differ from the classical maximal or reduced crossed products. online

Research Interests

Research Interests

$\bullet$ Operatoralgebren und nichtkommutative Geometrie

Selected Publications

Selected Publications of Siegfried Echterhoff

$\bullet$ A. Buss, S. Echterhoff, and R. Willett. Exotic crossed products and the Baum- Connes conjecture. J. Reine Angew. Math., 740:111–159, 2018.

$\bullet$ J. Cuntz, S. Echterhoff, and X. Li. On the K-theory of the C*-algebra generated by the left regular representation of an Ore semigroup. J. Eur. Math. Soc. (JEMS), 17(3):645–687, 2015.

$\bullet$ J. Cuntz, S. Echterhoff, and X. Li. On the $K$-theory of crossed products by automorphic semigroup actions. Q. J. Math., 64(3):747–784, 2013.

$\bullet$ S. Echterhoff, W. Lück, N. C. Phillips, and S. Walters. The structure of crossed products of irrational rotation algebras by finite subgroups of ${\rm SL}_2(\Bbb Z)$. J. Reine Angew. Math., 639:173–221, 2010.

$\bullet$ S. Echterhoff, S. Kaliszewski, J. Quigg, and I. Raeburn. A categorical approach to imprimitivity theorems for $C^*$-dynamical systems. Mem. Amer. Math. Soc., 180(850):viii+169, 2006.

$\bullet$ J. Chabert, S. Echterhoff, and H. Oyono-Oyono. Going-down functors, the Künneth formula, and the Baum-Connes conjecture. Geom. Funct. Anal., 14(3):491–528, 2004.

$\bullet$ J. Chabert, S. Echterhoff, and R. Nest. The Connes- Kasparov conjecture for almost connected groups and for linear $p$-adic groups. Publ. Math. Inst. Hautes \'Etudes Sci., (97):239–278, 2003.

$\bullet$ J. Chabert and S. Echterhoff. Permanence properties of the Baum- Connes conjecture. Doc. Math., 6:127–183, 2001.

$\bullet$ S. Echterhoff and D. P. Williams. Crossed products by $C_0(X)$-actions. J. Funct. Anal., 158(1):113–151, 1998.

$\bullet$ S. Echterhoff. Crossed products with continuous trace. Mem. Amer. Math. Soc., 123(586):viii+134, 1996.

Current Publications

$\bullet $ Siegfried Echterhoff and Mikael Rørdam. Inclusions of $C^*$-algebras arising from fixed-point algebras. arXiv e-prints, August 2021. arXiv:2108.08832.

$\bullet $ Bachir Bekka and Siegfried Echterhoff. On unitary representations of algebraic groups over local fields. Representation Theory, 25:508–526, June 2021. doi:10.1090/ert/574.

$\bullet $ Massoud Amini, Siegfried Echterhoff, and Hamed Nikpey. $C^\ast $-operator systems and crossed products. Journal of Mathematical Analysis and Applications, 491(1):124308, November 2020. doi:10.1016/j.jmaa.2020.124308.

$\bullet $ Alcides Buss, Siegfried Echterhoff, and Rufus Willett. The maximal injective crossed product. Ergodic Theory and Dynamical Systems, 40(11):2995–3014, November 2020. doi:10.1017/etds.2019.25.

$\bullet $ Alcides Buss, Siegfried Echterhoff, and Rufus Willett. Injectivity, crossed products, and amenable group actions. In $K$-theory in algebra, analysis and topology, volume 749 of Contemp. Math., pages 105–137. May 2020. doi:10.1090/conm/749/15069.

$\bullet $ Alcides Buss, Siegfried Echterhoff, and Rufus Willett. Amenability and weak containment for actions of locally compact groups on $C^*$-algebras. arXiv e-prints, March 2020. arXiv:2003.03469.