RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2004, Volume 75, Issue 2, Pages 208–221 (Mi mz24)

Commutative Subalgebras of Quantum Algebras

S. A. Zelenova

M. V. Lomonosov Moscow State University

Abstract: In the present paper, a general assertion is proved, claiming that, for every associative algebra $\mathscr A$ without zero divisors which admits a valuation and a seminorm concordant with the valuation, the transcendence degree of an arbitrary commutative subalgebra does not exceed the maximal number of independent pairwise pseudocommuting elements of some basis of the algebra $\mathscr A$. The author shows that for such a algebra $\mathscr A$ one can take an arbitrary algebra of quantum Laurent polynomials, quantum analogs of the Weyl algebra, and also some universal coacting algebras. In the case of the algebra $\mathscr L$ of quantum Laurent polynomials, it is proved that the transcendence degree of a maximal commutative subalgebra of $\mathscr L$ coincides with the maximal number of independent pairwise commuting elements of the monomial basis of the algebra $\mathscr L$.

DOI: https://doi.org/10.4213/mzm24

Full text: PDF file (246 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2004, 75:2, 190–201

Bibliographic databases:

UDC: 512.552

Citation: S. A. Zelenova, “Commutative Subalgebras of Quantum Algebras”, Mat. Zametki, 75:2 (2004), 208–221; Math. Notes, 75:2 (2004), 190–201

Citation in format AMSBIB
\Bibitem{Zel04} \by S.~A.~Zelenova \paper Commutative Subalgebras of Quantum Algebras \jour Mat. Zametki \yr 2004 \vol 75 \issue 2 \pages 208--221 \mathnet{http://mi.mathnet.ru/mz24} \crossref{https://doi.org/10.4213/mzm24} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2054553} \zmath{https://zbmath.org/?q=an:1111.16042} \elib{http://elibrary.ru/item.asp?id=13446763} \transl \jour Math. Notes \yr 2004 \vol 75 \issue 2 \pages 190--201 \crossref{https://doi.org/10.1023/B:MATN.0000015035.96781.1c} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000220006100020}