RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue 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

 TMF: Year: Volume: Issue: Page: Find

 TMF, 2005, Volume 144, Number 3, Pages 513–543 (Mi tmf1874)

dS–AdS Structures in Noncommutative Minkowski Spaces

M. A. Olshanetskyab, V.-B. K. Rogovc

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b University of Aarhus
c Moscow State University of Railway Communications

Abstract: We consider a family of noncommutative four-dimensional Minkowski spaces with the signature $(1,3)$ and two types of spaces with the signature $(2,2)$. The Minkowski spaces are defined by the common reflection equation and differ in anti-involutions. There exist two Casimir elements, and. xing one of them leads to the noncommutative “homogeneous” spaces $H_3$, $dS_3$, $AdS_3$, and light cones. We present a semiclassical description of the Minkowski spaces. There are three compatible Poisson structures: quadratic, linear, and canonical. Quantizing the first leads to the Minkowski spaces. We introduce horospheric generators of the Minkowski spaces, and they lead to the horospheric description of $H_3$, $dS_3$, and $AdS_3$. We construct irreducible representations of the Minkowski spaces $H_3$ and $dS_3$. We find eigenfunctions of the Klein–Gordon equation in terms of the horospheric generators of the Minkowski spaces, and they lead to eigenfunctions on $H_3$, $dS_3$, $AdS_3$, and light cones.

Keywords: noncommutative geometry, Yang–Baxter equation, reflection equation, harmonic analysis on noncommutative spaces

DOI: https://doi.org/10.4213/tmf1874

Full text: PDF file (401 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2005, 144:3, 1315–1343

Bibliographic databases:

Citation: M. A. Olshanetsky, V.-B. K. Rogov, “dS–AdS Structures in Noncommutative Minkowski Spaces”, TMF, 144:3 (2005), 513–543; Theoret. and Math. Phys., 144:3 (2005), 1315–1343

Citation in format AMSBIB
\Bibitem{OlsRog05} \by M.~A.~Olshanetsky, V.-B.~K.~Rogov \paper dS--AdS Structures in Noncommutative Minkowski Spaces \jour TMF \yr 2005 \vol 144 \issue 3 \pages 513--543 \mathnet{http://mi.mathnet.ru/tmf1874} \crossref{https://doi.org/10.4213/tmf1874} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2191845} \zmath{https://zbmath.org/?q=an:1178.81260} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2005TMP...144.1315O} \elib{http://elibrary.ru/item.asp?id=9155037} \transl \jour Theoret. and Math. Phys. \yr 2005 \vol 144 \issue 3 \pages 1315--1343 \crossref{https://doi.org/10.1007/s11232-005-0162-2} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000232646400006}