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Probabilistyka na topologicznych grupach kwantowych

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163--196
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Bibliogr. 42 poz.
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Bibliografia
  • [1] L. Accardi, M. Schürmann, W. von Waldenfels, Quantum independent increment processes on superalgebras, Math. Z. 198 (1988), no. 4, 451-477.
  • [2] D. Applebaum, Lévy processes and stochastic calculus, Cambridge Studies in Advanced Mathematics, vol. 93, Cambridge University Press, Cambridge 2004.
  • [3] D. Applebaum, Lévy processes-from probability to finance and quantum groups, Notices Amer. Math. Soc. 51 (2004), no. 11, 1336-1347.
  • [4] W. Arveson, Noncommutative dynamics and E-semigroups, Springer Monographs in Mathematics, Springer-Verlag, New York 2003.
  • [5] J. Bertoin, Lévy processes, Cambridge Tracts in Mathematics, vol. 121, Cambridge University Press, Cambridge 1996.
  • [6] W. R. Bloom, H. Heyer, Harmonic analysis of probability measures on hypergroups, de Gruyter Studies in Mathematics, vol. 20,Walter de Gruyter & Co., Berlin 1995.
  • [7] Yu. A. Chapovsky, L. I. Vainerman, Compact quantum hypergroups, J. Operator Theory 41 (1999), no. 2, 261-289.
  • [8] A. Connes, Noncommutative geometry, Academic Press Inc., San Diego, CA 1994.
  • [9] E. G. Effros, Z.-J. Ruan, Operator spaces, London Mathematical Society Monographs. New Series, vol. 23, The Clarendon Press Oxford University Press, New York 2000.
  • [10] U. Franz, Lévy processes on quantum groups and dual groups, Quantum independent increment processes. II, Lecture Notes in Math., vol. 1866, Springer, Berlin, 2006, 161-257.
  • [11] U. Franz, A. Skalski, R. Tomatsu, Classification of idempotent states on the compact quantum groups Uq(2), SUq(2), and SOq(3), dostępne pod adresem arXiv:0903.2363v1[math.OA].
  • [12] U. Franz, A. Skalski, On ergodic properties of convolution operators associated with compact quantum groups, Colloq. Math. 113 (2008), no. 1, 13-23.
  • [13] U. Franz, A. Skalski, On idempotent states on quantum groups, J. Algebra 322 (2009), no. 5, 1774-1802.
  • [14] U. Franz, A. Skalski, A new characterisation of idempotent states on finite and compact quantum groups, C. R. Math. Acad. Sci. Paris 347 (2009), no. 17-18, 991-996.
  • [15] U. Grenander, Probabilities on algebraic structures, John Wiley & Sons Inc., New York 1963.
  • [16] P. Hayden, A. Winter, Counterexamples to the maximal p-norm multiplicitym conjecture for all p > 1, Comm. Math. Phys. 284 (2008), no. 1, 263-280.
  • [17] H. Heyer, Probability measures on locally compact groups, Springer-Verlag, Berlin 1977. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 94.
  • [18] H. Heyer, Structural aspects in the theory of probability, Series on Multivariate Analysis, vol. 7, World Scientific Publishing Co. Inc., River Edge, NJ 2004. A primer in probabilities on algebraic-topological structures.
  • [19] R. L. Hudson, K. R. Parthasarathy, Quantum Ito's formula and stochastic evolutions, Comm. Math. Phys. 93 (1984), no. 3, 301-323.
  • [20] V. Jones, V. S. Sunder, Introduction to subfactors, London Mathematical Society Lecture Note Series, vol. 234, Cambridge University Press, Cambridge 1997.
  • [21] M. Junge, Q. Xu, Noncommutative maximal ergodic theorems, J. Amer. Math. Soc. 20 (2007), no. 2, 385-439.
  • [22] G. I. Kac, Group extensions which are ring groups, Mat. Sb. (N.S.) 76 (118) (1968), 473-496.
  • [23] A. Klimyk, K. Schmüdgen, Quantum groups and their representations, Texts and Monographs in Physics, Springer-Verlag, Berlin 1997.
  • [24] L. I. Korogodski, Y. S. Soibelman, Algebras of functions on quantum groups. Part I, Mathematical Surveys and Monographs, vol. 56, American Mathematical Society, Providence, RI 1998.
  • [25] J. Kustermans, S. Vaes, Locally compact quantum groups, Ann. Sci. école Norm. Sup. (4) 33 (2000), no. 6, 837-934.
  • [26] J. Kustermans, Locally compact quantum groups, Quantum independent increment processes. I, Lecture Notes in Math., vol. 1865, Springer, Berlin, 2005, 99-180.
  • [27] J. M. Lindsay, A. Skalski, On convolution semigroups of states, ukaże się w Math. Z.
  • [28] J. M. Lindsay, Quantum stochastic analysis-an introduction, Quantum independent increment processes. I, Lecture Notes in Math., vol. 1865, Springer, Berlin, 2005, 181-271.
  • [29] J. M. Lindsay, A. G. Skalski, Quantum stochastic convolution cocycles. II, Comm. Math. Phys. 280 (2008), no. 3, 575-610.
  • [30] P. Mankiewicz, N. Tomczak-Jaegermann, Quotients of finite-dimensional Banach spaces; random phenomena, Handbook of the geometry of Banach spaces, Vol. 2, North-Holland, Amsterdam, 2003, 1201-1246.
  • [31] T. Masuda, Y. Nakagami, S. L. Woronowicz, A C_-algebraic framework for quantum groups, Internat. J. Math. 14 (2003), no. 9, 903-1001.
  • [32] P.-A. Meyer, Quantum probability for probabilists, Lecture Notes in Mathematics, vol. 1538, Springer-Verlag, Berlin 1993.
  • [33] A. Pal, A counterexample on idempotent states on a compact quantum group, Lett. Math. Phys. 37 (1996), no. 1, 75-77.
  • [34] K. R. Parthasarathy, An introduction to quantum stochastic calculus, Monographs in Mathematics, vol. 85, Birkh¨auser Verlag, Basel 1992.
  • [35] G. K. Pedersen, C_-algebras and their automorphism groups, London Mathematical Society Monographs, vol. 14, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], London 1979.
  • [36] P. Podles, Symmetries of quantum spaces. Subgroups and quotient spaces of quantum SU(2) and SO(3) groups, Comm. Math. Phys. 170 (1995), no. 1, 1-20.
  • [37] M. Schürmann, White noise on bialgebras, Lecture Notes in Mathematics, vol. 1544, Springer-Verlag, Berlin 1993.
  • [38] M. Schürmann, M. Skeide, Infinitesimal generators on the quantum group SUq(2), Infin. Dimens. Anal. Quantum Probab. Relat. Top. 1 (1998), no. 4, 573-598.
  • [39] A. Van Daele, The Haar measure on finite quantum groups, Proc. Amer. Math. Soc. 125 (1997), no. 12, 3489-3500.
  • [40] S. L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys. 111 (1987), no. 4, 613-665.
  • [41] S. L.Woronowicz, Tannaka-Kre˘ın duality for compact matrix pseudogroups. Twisted SU(N) groups, Invent. Math. 93 (1988), no. 1, 35-76.
  • [42] S. L. Woronowicz, Compact quantum groups, Symétries quantiques (Les Houches, 1995), North-Holland, Amsterdam, 1998, 845-884.
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Bibliografia
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bwmeta1.element.baztech-article-BUS8-0012-0058
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