Noncommutative Mathematics for Quantum Systems

(Dana P.) #1
References 119

EMS Textbooks in Mathematics. European Mathematical Society
(EMS), Zurich, 2008. ̈

[Ulr14] M. Ulrich. Construction of a free Levy process as high-dimensional ́
limit of a Brownian motion on the Unitary group. Preprint arXiv:
1407.0212v1, 2014. To appear in Inf. Dim. Anal., Quantum Prob. and
Rel. Topics.


[VD97] A. Van Daele, The Haar measure on finite quantum groups. Proc.
Amer. Math. Soc., 125(12): 3489–3500, 1997.


[VD98] A. Van Daele. An algebraic framework for group duality. Adv.
Math., 140(2): 323–366, 1998.


[VD03] A. Van Daele. Multiplier Hopf∗-algebras with positive integrals: a
laboratory for locally compact quantum groups. Vainerman, Leonid
(ed.), Locally compact quantum groups and groupoids. Proceedings
of the 69th meeting of theoretical physicists and mathematicians,
Strasbourg, France, February 21–23, 2002. Berlin: Walter de Gruyter.
IRMA Lect. Math. Theor. Phys. 2, 229–247 (2003)., 2003.


[VDN92] D. Voiculescu, K. Dykema, and A. Nica.Free Random Variables.
AMS, 1992.


[VDW96] A. Van Daele and Shuzhou Wang. Universal quantum groups.
Internat. J. Math., 7(2): 255–263, 1996.


[Voi86] D. Voiculescu. Addition of certain noncommuting random variables.
J. Funct. Anal., 66(3): 323–346, 1986.


[Voi87] D. Voiculescu. Dual algebraic structures on operator algebras related
to free products.J. Oper. Theory, 17: 85–98, 1987.


[Voi90] D. Voiculescu. Noncommutative random variables and spectral
problems in free productC∗-algebras.Rocky Mountain J. Math.,
20(2): 263–283, 1990.


[Voi91] D. Voiculescu. Limit laws for random matrices and free products.
Invent. Math.104 (1991), no. 1, 201–220.


[Voi00] D. Voiculescu. Lectures on free probability theory. In:Lectures on
probability theory and statistics (Saint-Flour, 1998), pp. 279–
349, Lecture Notes in Math., 1738, Springer, Berlin, 2000.


[Voi11] C. Voigt. The Baum-Connes conjecture for free orthogonal quantum
groups.Adv. Math., 227(5): 1873–1913, 2011.


[Vos13] S. Voß. Realisierung von Quantum-Levy-Prozessen auf Fockr ́ aumen. ̈
Ph.D. Thesis, Ernst-Moritz-Arndt-Universit ̈at Greifswald, 2013.

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