Itô calculus and quantisation of Lie bialgebras

R. L. Hudson

Annales de l'I.H.P. Probabilités et statistiques (2005)

  • Volume: 41, Issue: 3, page 375-390
  • ISSN: 0246-0203

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Hudson, R. L.. "Itô calculus and quantisation of Lie bialgebras." Annales de l'I.H.P. Probabilités et statistiques 41.3 (2005): 375-390. <http://eudml.org/doc/77850>.

@article{Hudson2005,
author = {Hudson, R. L.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
language = {eng},
number = {3},
pages = {375-390},
publisher = {Elsevier},
title = {Itô calculus and quantisation of Lie bialgebras},
url = {http://eudml.org/doc/77850},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Hudson, R. L.
TI - Itô calculus and quantisation of Lie bialgebras
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2005
PB - Elsevier
VL - 41
IS - 3
SP - 375
EP - 390
LA - eng
UR - http://eudml.org/doc/77850
ER -

References

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  1. [1] L. Accardi, A. Frigerio, J.T. Lewis, Quantum stochastic processes, Publ. RIMS Kyoto18 (1982) 97-133. Zbl0498.60099MR660823
  2. [2] B. Enriquez, Quantisation of Lie bialgebras and shuffle algebras of Lie algebras, Selecta Math. (N.S.)7 (2001) 321-407. Zbl1009.17010MR1868300
  3. [3] P. Etingof, D. Kazhdan, Quantization of Lie bialgebras, I, Selecta Math. (NS.)2 (1966) 1-41. Zbl0863.17008MR1403351
  4. [4] R.L. Hudson, Calculus in enveloping algebras, J. London Math. Soc. (2)65 (2002) 361-380. Zbl1010.17009MR1883188
  5. [5] R.L. Hudson, K.R. Parthasarathy, Quantum Itô's formula and stochastic evolutions, Commun. Math. Phys.93 (1984) 301-323. Zbl0546.60058MR745686
  6. [6] R.L. Hudson, K.R. Parthasarathy, S. Pulmannová, The method of formal power series in quantum stochastic calculus, IDAQP3 (2000) 387-401. Zbl0968.60101MR1811249
  7. [7] R.L. Hudson, S. Pulmannová, Double product integrals and Enriquez quantisation of Lie bialgebras I: the quasitriangularity relations, J. Math. Phys.45 (2004) 2090-2105. Zbl1071.81073MR2054150
  8. [8] R.L. Hudson, S. Pulmannová, Double product integrals and Enriquez quantisation of Lie bialgebras II: the quantum Yang–Baxter equation, Lett. Math. Phys., submitted for publication. Zbl1079.53139MR2164611
  9. [9] R.L. Hudson, S. Pulmannová, Symmetrized double quantum stochastic product integrals, J. Math. Phys.41 (2000) 8249-8262. Zbl0985.81053MR1797319
  10. [10] P.A. Meyer, Quantum Probability for Probabilists, Lecture Notes in Math., vol. 1538, Springer, 1993. Zbl0773.60098MR1222649
  11. [11] R.F. Streater, Current commutation relations, continuous tensor products and infinitely divisible group representations, Rend. Sc. Inst. Fisica E. FermiXI (1969) 247-263. 

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