Skip to main content

Gaussian states on bialgebras

  • Conference paper
  • First Online:
Quantum Probability and Applications V

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1442))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abe, E.: Hopf algebras. Cambridge: Cambridge University Press 1980

    MATH  Google Scholar 

  2. Accardi, L., Schürmann, M., Waldenfels, W.v.: Quantum independent increment processes on superalgebras. Math. Z. 198, 451–477 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  3. Araki, H.: Factorizable representation of current algebra. Publ. Res. Inst. Math. Sci. 5, 361–422 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  4. Glockner, P.: *-Bialgebren in der Quantenstochastik. Dissertation, Heidelberg 1989

    Google Scholar 

  5. Glockner, P., Waldenfels, W.v.: The relations of the non-commutative coefficient algebra of the unitary group. SFB-Preprint Nr. 460, Heidelberg 1988

    Google Scholar 

  6. Guichardet, A.: Symmetric Hilbert spaces and related topics. (Lect. Notes Math. vol. 261). Berlin Heidelberg New York: Springer 1972

    MATH  Google Scholar 

  7. Heyer, H.: Probability measures on locally compact groups. Berlin Heidelberg New York: Springer 1977

    Book  MATH  Google Scholar 

  8. Hudson, R.L., Parthasarathy, K.R.: Quantum Ito’s formula and stochastic evolutions. Commun. Math. Phys. 93, 301–323 (1984)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Hunt, G.A.: Semi-groups of measures on Lie groups. Trans. Amer. Math. Soc. 81, 264–293 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  10. Mathon, D., Streater, R.F.: Infinitely divisible representations of Clifford algebras. Z. Wahrscheinlichkeitstheorie verw. Geb. 20, 308–316 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  11. Schürmann, M.: Positive and conditionally positive linear functionals on coalgebras. In: Accardi, L., Waldenfels, W.v. (eds) Quantum Probability and Applications II. Proceedings, Heidelberg 1984. (Lect. Notes Math., vol. 1136). Berlin Heidelberg New York: Springer 1985

    Google Scholar 

  12. Schürmann, M.: Noncommutative stochastic processes with independent and stationary increments satisfy quantum stochastic differential equations. To appear in Probab. Th. Rel. Fields

    Google Scholar 

  13. Schürmann, M: A class of representations of involutive bialgebras. To appear in Math. Proc. Cambridge Philos. Soc.

    Google Scholar 

  14. Schürmann, M.: Quantum stochastic processes with independent additive increments. Preprint, Heidelberg 1989

    MATH  Google Scholar 

  15. Streater, R.F.: Infinitely divisible representations of Lie algebras. Z. Wahrscheinlichkeitstheorie verw. Geb. 42, 67–80 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  16. Sweedler, M.E.: Hopf algebras. New York: Benjamin 1969

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Luigi Accardi Wilhelm von Waldenfels

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag

About this paper

Cite this paper

Schürmann, M. (1990). Gaussian states on bialgebras. In: Accardi, L., von Waldenfels, W. (eds) Quantum Probability and Applications V. Lecture Notes in Mathematics, vol 1442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085528

Download citation

  • DOI: https://doi.org/10.1007/BFb0085528

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53026-8

  • Online ISBN: 978-3-540-46311-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics