Itô versus Woronowicz calculus in Itô Hopf algebras

Robin L. Hudson

Mathematica Slovaca (2004)

  • Volume: 54, Issue: 2, page 151-159
  • ISSN: 0232-0525

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Hudson, Robin L.. "Itô versus Woronowicz calculus in Itô Hopf algebras." Mathematica Slovaca 54.2 (2004): 151-159. <http://eudml.org/doc/32002>.

@article{Hudson2004,
author = {Hudson, Robin L.},
journal = {Mathematica Slovaca},
keywords = {Itô calculus; Hopf algebras; quantum stochastics},
language = {eng},
number = {2},
pages = {151-159},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Itô versus Woronowicz calculus in Itô Hopf algebras},
url = {http://eudml.org/doc/32002},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Hudson, Robin L.
TI - Itô versus Woronowicz calculus in Itô Hopf algebras
JO - Mathematica Slovaca
PY - 2004
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 54
IS - 2
SP - 151
EP - 159
LA - eng
KW - Itô calculus; Hopf algebras; quantum stochastics
UR - http://eudml.org/doc/32002
ER -

References

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  1. ENRIQUEZ B., Quantization of Lie bialgebras and shuffle algebras of Lie algebras, Selecta Math. (N.S.) 7 (2001), 321-407. Zbl1009.17010MR1868300
  2. ETINGOF P.-KAZHDAN D., Quantization of Lie bialgebras I, Selecta Math. (N.S.) 2 (1996), 1-41. (1996) Zbl0863.17008MR1403351
  3. ETINGOF P.-SCHIFFMAN O., Lectures on Quantum Groups, International Press, Cambridge, MA, 1998. (1998) Zbl1105.17300MR1698405
  4. HUDSON R. L., Calculus in enveloping algebras, J. London Math. Soc. (2) 65 (2001), 361-380. Zbl1010.17009MR1883188
  5. HUDSON R. L.-PARTHASARATHY K. R., Quantum Ito's formula and stochastic evolutions, Comm. Math. Phys. 93 (1984), 301-323. (1984) Zbl0546.60058MR0745686
  6. HUDSON R. L.-PULMANNOVÁ S., Chaotic expansions of elements of the universal enveloping algebra of a Lie algebra associated with a quantum stochastic calculus, Proc. London Math. Soc. (3) 77 (1998), 462-480. (1998) MR1635169
  7. HUDSON R. L.-PULMANNOVÁ S., Double productintegrals and Enriquex quantisation of Lie bialgebras I: The quasitriangularity relations, J. Math. Phys. (To appear); II: The quantum Yang-Baxter equation. Nottingham Trent Preprint 2003. 
  8. PARTHASARATHY K. R., An Introduction to Quantum Stochastic Calculus, Monogr. Math. 85, Birkhauser, Basel, 1992. (1992) Zbl0751.60046MR1164866
  9. WORONOWICZ S. L., Differential calculus on compact matrix pseudogroups, Comm. Math. Phys. 122 (1989), 125-170. (1989) Zbl0751.58042MR0994499

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