Skip to main content
SpringerLink
Log in

The Brauer group of Azumaya–Poisson S-algebras

  • Original Paper
  • Published:
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Aims and scope Submit manuscript

Abstract

In this paper we define the notion of Brauer group for Azumaya–Poisson S-algebras. This Brauer group turns out to be an example of a Brauer group of a symmetric monoidal category.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Auslander, M., Goldman, O.: The Brauer group of a commutative ring, 367–409. Trans. Am. Math. Soc. 97, 307–409 (1960)

    Google Scholar 

  • Caenepeel, S.: A cohomological interpretation of the Brauer Groups I. Comm. Algebra 11, 2129–2149 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  • Caenepeel, S.: Brauer Groups, Hopf Algebras and Galois Theory, \(K\)-Monographs Math, vol. 4. Kluwer Academic, Dordrecht (1998)

    Book  MATH  Google Scholar 

  • Caenepeel, S., Van Oystaeyen, F.: Brauer Groups and the Cohomology of Graded Rings, Monographs and Textbooks in Pure and App, vol. 121. Math. Marcel Dekker, New York (1988). ISBN 0-8247-7978-9, 261+x p

    MATH  Google Scholar 

  • DeMeyer, F.: An action of the automorphism group of a commutative ring on its Brauer group. Pac. J. Math. 97(2), 327–338 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  • DeMeyer, F., Ingraham, E.: Separable Algebras over Commutative Rings. Springer, Berlin (1971)

    Book  MATH  Google Scholar 

  • Guédénon, T.: Sur la cohomologie \(g\)-finie. Comm. Algebra 21(4), 1103–1139 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  • Guédénon, T.: On the \(H\)-finite cohomology. J. Algebra 273, 455–488 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Guédénon, T., Herman, A.: The Brauer-Clifford group for \((S, H)\)-Azumaya algebras over a commutative ring. Algebras Rep. Theory 16(1), 101–127 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  • Knus, M.-A., Ojanguren, M.: Théorie de la Descente et Algèbres d’Azumaya, vol. 389. Springer, Berlin (1974)

    Book  MATH  Google Scholar 

  • MacLane, S.: Categories for the Working Mathematician. Springer, Berlin (1971)

    MATH  Google Scholar 

  • Montgomery, S.: Hopf algebras and their actions on rings, CBMS Reg. Conf. Ser. in Math. 82, AMS (1993)

  • Oh, S.-Q.: Symplectic ideals of Poisson algebras and the Poisson structure associated to quantum matrices. Comm. Algebra 27(5), 2163–2180 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • Pareigis, B.: The Brauer group of a symmetric monoidal category. In: Zelinsky, D. (ed.) Brauer Groups, Evanston 1975, Lecture Notes in Math., 549. Springer, Berlin (1976)

    Google Scholar 

  • Pareigis, B.: Non additive ring and module theory I. General theory of monoids. Publicationes Mathematicae., 24 Kotet Debrecen, pp. 189–204 (1977)

  • Sweedler, M.: Hopf Algebras. Benjamin, New York (1969)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département de Mathématiques, Université de Ziguinchor, Ziguinchor, Sénégal

    T. Guédénon

Authors
  1. T. Guédénon
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Guédénon.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guédénon, T. The Brauer group of Azumaya–Poisson S-algebras. Beitr Algebra Geom 60, 571–585 (2019). https://doi.org/10.1007/s13366-019-00433-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13366-019-00433-2

Keywords

Mathematics Subject Classification

Search

Navigation