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TMF, 2010, Volume 164, Number 1, Pages 28–45 (Mi tmf6522)  

This article is cited in 1 scientific paper (total in 1 paper)

Quantum $s\ell(2)$ action on a divided-power quantum plane at even roots of unity

A. M. Semikhatov

Lebedev Physical Institute, RAS, Moscow, Russia

Abstract: We describe a nonstandard version of the quantum plane in which the basis is given by divided powers at an even root of unity $\mathfrak q=e^{i\pi/p}$. It can be regarded as an extension of the "nearly commutative" algebra $\mathbb C[X,Y]$ with $XY=(-1)^pYX$ by nilpotents. For this quantum plane, we construct a Wess–Zumino-type de Rham complex and find its decomposition into representations of the $2p^3$-dimensional quantum group $\overline{\mathcal U}_{\mathfrak q}s\ell(2)$ and its Lusztig extension $\boldsymbol{\mathcal U}_{\mathfrak q}s\ell(2)$; we also define the quantum group action on the algebra of quantum differential operators on the quantum plane.

Keywords: quantum plane, divided power, Lusztig quantum group, indecomposable representation

DOI: https://doi.org/10.4213/tmf6522

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English version:
Theoretical and Mathematical Physics, 2010, 164:1, 853–868

Bibliographic databases:

Document Type: Article
Received: 07.09.2009
Revised: 24.12.2009

Citation: A. M. Semikhatov, “Quantum $s\ell(2)$ action on a divided-power quantum plane at even roots of unity”, TMF, 164:1 (2010), 28–45; Theoret. and Math. Phys., 164:1 (2010), 853–868

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6522
  • http://mi.mathnet.ru/eng/tmf/v164/i1/p28

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Gu H. Hu N., “Loewy Filtration and Quantum de Rham Cohomology Over Quantum Divided Power Algebra”, J. Algebra, 435 (2015), 1–32  crossref  mathscinet  zmath  isi  elib  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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