Kontakt
Forschungsgebiete
Publikationen

Fakultät
Mathematisches Institut
Abteilung 


  Monographs
  • Unbounded Operator Algebras and Representation Theory. Akademie-Verlag Berlin and Birkhäuser-Verlag Basel, 1990. 380pp
  • (with A.U. Klimyk) Quantum Groups and Their Representations. Texts and Monographs in Physics, Springer-Verlag Heidelberg, 1997. 552 pp.
  Publications

    Noncommutative real algebraic geometry
  • A strict Positivstellensatz for the Weyl algebra. Math. Ann. 331, 779-794; arxiv
  • A strict Positivstellensatz for Enveloping algebras. Math. Z. 254(2006) 641-653; Erratum: Math. Z. 259(2008) 231; arxiv
  • Noncommutative real algebraic geometry - some basic concepts and first ideas; In: Emerging applications of algebraic geometry. M. Putinar and S. Sullivant (eds.), Springer 2009; arxiv
  • Algebras of fractions and strict Positivstellensätze for *-Algebras, 20pp., 2009; arxiv
  • (with Y. Savchuk) A noncommutative version of the Fejér-Riesz theorem, to appear in Proc. Amer. Math. Soc; arxiv
    Quantum groups and noncommutative geometry
  • (with A. Schüler) Classification of bicovariant differential calculi on quantum groups of type A,B,C and D. Commun. Math. Phys. 167, 635-670 (1995).
  • (with A.Schüler) Classification of bicovariant differential calculi on quantum linear groups. Commun. Math. Phys. 170, 315-335 (1995).
  • (with A. Schüler) Left-covariant differential calculi on SLq(2) and SLq(3). J. Geom. Phys. 20, 87-115 (1996)
  • (with I. Heckenberger) Levi-Civita connections on the quantum groups SLq(N), Oq(N) and Spq(N). Commun. Math. Phys. 185, 177-196 (1997)
  • (with I. Heckenberger) Classification of bicovariant differential calculi on the quantum groups SLq(n+1) and Spq(2n). J. Reine Angew. Math. 502, 141-162 (1998)
  • Commutator representations of differential calculi on the quantum group SUq(2). J. Geom. Phys. 31, 241-264 (1999)
  • A polar decomposition for holomorphic functions on a strip. Bull. London Math. Soc.  33, 309-319 (2001)
  • Commutator representations of covariant differential calculi on quantum groups. Lett. Math. Phys. 59, 95-106 (2002)
  • The quantum quarter plane and the real quantum plane. Internat. J. Math. 13, 279-321 (2002)
  • (with E. Wagner) Examples of twisted cyclic cocycles from covariant differetial calculi. Lett. Math. Phys. 64, 245-254 (2003)
  • (with E. Wagner) Dirac operator and a twisted cyclic cocycle on the standard Podles quantum sphere. J. Reine Angew. Math. 574, 219-235 (2004)
    Unbounded operators and unbounded representations
  • Integrable operator representations of R_q2, Xq, and SLq(2,R). Commun. Math. Phys. 159, 217-237 (1994)
  • Operator representations of Uq(sl_(R)). Lett. Math. Phys. 37, 211-222 (1996)
  • Operator representations of a q-deformed Heisenberg algebra. J. Math. Phys. 40, 4596-4604 (1999)
  • On well-behaved representations of *-algebras. J. Operator Theory 48, 287-502 (2002)
  • (with S. Ota) Some self-adjoint 2x2 operator matrices associated with closed operators. Integral Equations Operator Theory 45, 475-484 (2003)
  • (with E. Wagner) Hilbert space representations of cross product algebras. J. Funct. Anal.  200, 451-493 (2003)
  • (with E. Wagner) Hilbert space representations of cross product algebras II. Algebr. Repres. Theory 9(2006) 431-464; arXiv math.GA/0308229
  • (with E. Wagner) Representations of cross product algebras with Podles spheres, J. Lie Theory 17(2007)751-790; arXiv math.QA/0305309
  • Unbounded operators affiliated with C*-algebras, Leipzig, 2003, unpublished.
  • (with Y. Savchuk) Unbounded Induced Representations of *-Algebras, preprint; arxiv
    Multidimensional moment problems
  • The K-moment problem for compact semi-algebraic sets. Math. Ann. 289, 203-206 (1991)
  • On determinacy notions for the two dimensional moment problem. Arkiv für Mat. 29, 277-284 (1991)
  • Non-commutative moment problems. Math. Z. 206, 623-650 (1991)
  • On the moment problem of closed semi-algebraic sets. J. Reine Angew. Math. 558, 225-234 (2003)
  • (with M. Putinar) Multivariate Determinateness. Indiana Univ. Math. J. 57, 2931-2986 (2008), arxiv