Berndt Brenken

Professor Emeritus

Department of Mathematics and Statistics


University of Pennsylvania, 1982


University of Pennsylvania, 1979

BSc (Hons)

University of Toronto, 1977

Contact information


Office: 403.220.3948


Office : MS440

Office hours

By appointment


  • MATH 331 - Advanced Calculus for the Natural Sciences
  • MATH 367 - University Calculus III

Research and teaching

Research areas

  • Operator algebras
  • K-theory
  • C*-algebras
  • C*-dynamical systems
  • Topological directed graphs
  • Functional analysis
  • Completely positive maps



  • Brenken, B., Cuntz, Joachim, Elliott, George A. and Nest, Ryszard. On the classification of noncommutative tori. {III} 62. Amer. Math. Soc., 1987. 503-526. Print.

Journal article

  • Brenken, B.. "Topological quivers as multiplicity free relations". Mathematica Scandinavica 106.2 (2010): 217-242. Print.
  • Brenken, B.. "The isolated ideal of a correspondence associated with a topological quiver". New York Journal of Mathematics 12.2006 (2006): 47-62. Print.
  • Brenken, B.. "{$C\sp *$}-algebras associated with topological relations". Journal of the Ramanujan Mathematical Society 19.1 (2004): 35-55. Print.
  • Brenken, B.. "Endomorphisms of type {I} von {N}eumann algebras with discrete center". Journal of Operator Theory 51.1 (2004): 19-34. Print.
  • Brenken, B.. "$Csp *$-algebras of infinite graphs and Cuntz-Krieger algebras". Canadian Mathematical Bulletin. Bulletin Canadien de Mathematiques 45.3 (2002): 321-336. Print.
  • Brenken, B.. "Cuntz-{K}rieger algebras and endomorphisms of finite direct sums of type {${\rm I}\sb \infty$} factors". Transactions of the American Mathematical Society 353.10 (2001): 3835-3873 (electronic). Print.
  • Brenken, B.. "Hecke algebras and semigroup crossed product {$C\sp *$}-algebras". Pacific Journal of Mathematics 187.2 (1999): 241-262. Print.
  • Brenken, B.. "The local product structure of expansive automorphisms of solenoids and their associated {$C\sp \ast$}-algebras". Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 48.4 (1996): 692-709. Print.
  • Brenken, B.. "{$K$}-groups of solenoidal algebras. {I}". Proc. Amer. Math. Soc. 123.5 (1995): 1457-1464. Print.
  • Brenken, B.. "Isomorphism classes of solenoidal algebras. {I}". Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 36.4 (1993): 414-418. Print.
  • Brenken, B. and Jorgensen, Palle E. T.. "A family of dilation crossed product algebras". Journal of Operator Theory 25.2 (1991): 299-308. Print.
  • Brenken, B.. "Classification of skew symmetric matrices". Proc. Amer. Math. Soc. 108.1 (1990): 163-169. Print.
  • Brenken, B.. "A classification of some noncommutative tori". The Rocky Mountain Journal of Mathematics 20.2 (1990): 389-397. Print.
  • Brenken, B.. "Norm limits of finite direct sums of {$I\sb \infty$} factors". Journal of Operator Theory 15.1 (1986): 3-13. Print.
  • Brenken, B.. "Approximately inner automorphisms of the irrational rotation algebra". La Soci\'et\'e Royale du Canada. L'Academie des Sciences. Comptes Rendus Math\'ematiques. (Mathematical Reports) 7.6 (1985): 363-368. Print.
  • Brenken, B.. "Representations and automorphisms of the irrational rotation algebra". Pacific Journal of Mathematics 111.2 (1984): 257-282. Print.

Journal articles - peer reviewed

  • Brenken, B.. "Completely Positive Contractive Maps and Partial Isometries". Advances in Operator Theory 3.1 (2018): 271 -294. Print.  
  • Brenken, B.. "Ordered *-semigroups and a C*-correspondence for a Partial Isometry". SIGMA 10. (2014): 50. Print.
  • Brenken, B. and Niu, Z. "The C*-algebra of a Partial Isometry". Proc. Amer. Math. Soc. 140.1 (2012): 199-206. Print.
  • Brenken, B.. "A Dynamical Core for Topological Directed Graphs". Muenster J Math. 3. (2010): 111-144. Print.