Algebra i Analiz
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra i Analiz:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Algebra i Analiz, 2006, Volume 18, Issue 5, Pages 156–172 (Mi aa92)  

This article is cited in 17 scientific papers (total in 17 papers)

Research Papers

On quantization of the Semenov–Tian–Shansky Poisson bracket on simple algebraic groups

A. Mudrovab

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b Department of Mathematics, University of York, UK
References:
Abstract: Let $G$ be a simple complex factorizable Poisson algebraic group. Let $\mathcal U_\hbar(\mathfrak g)$ be the corresponding quantum group. We study the $\mathcal U_\hbar(\mathfrak g)$-equivariant quantization $\mathcal C_\hbar[G]$ of the affine coordinate ring $\mathcal C[G]$ along the Semenov–Tian–Shansky bracket. For a simply connected group $G$, we give an elementary proof for the analog of the Kostant–Richardson theorem stating that $\mathcal C_\hbar[G]$ is a free module over its center.
Keywords: Poisson Lie manifolds, quantum groups, equivariant quantization.
Received: 22.04.2006
English version:
St. Petersburg Mathematical Journal, 2007, Volume 18, Issue 5, Pages 797–808
DOI: https://doi.org/10.1090/S1061-0022-07-00974-0
Bibliographic databases:
Document Type: Article
MSC: Primary 53Dxx; Secondary 20Gxx
Language: English
Citation: A. Mudrov, “On quantization of the Semenov–Tian–Shansky Poisson bracket on simple algebraic groups”, Algebra i Analiz, 18:5 (2006), 156–172; St. Petersburg Math. J., 18:5 (2007), 797–808
Citation in format AMSBIB
\Bibitem{Mud06}
\by A.~Mudrov
\paper On quantization of the Semenov--Tian--Shansky Poisson bracket on simple algebraic groups
\jour Algebra i Analiz
\yr 2006
\vol 18
\issue 5
\pages 156--172
\mathnet{http://mi.mathnet.ru/aa92}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2301044}
\zmath{https://zbmath.org/?q=an:1236.17025}
\transl
\jour St. Petersburg Math. J.
\yr 2007
\vol 18
\issue 5
\pages 797--808
\crossref{https://doi.org/10.1090/S1061-0022-07-00974-0}
Linking options:
  • https://www.mathnet.ru/eng/aa92
  • https://www.mathnet.ru/eng/aa/v18/i5/p156
  • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и анализ St. Petersburg Mathematical Journal
    Statistics & downloads:
    Abstract page:474
    Full-text PDF :146
    References:60
    First page:2
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024