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Teoreticheskaya i Matematicheskaya Fizika, 2000, Volume 124, Number 2, Pages 227–238
DOI: https://doi.org/10.4213/tmf635
(Mi tmf635)
 

This article is cited in 8 scientific papers (total in 8 papers)

Realization of Lie algebras and superalgebras in terms of creation and annihilation operators: I

Č. Burdíka, P. Ya. Grozmanb, D. A. Leitesb, A. N. Sergeevc

a Czech Technical University
b Stockholm University
c Balakovo Institute of Technique, Technology and Control
Full-text PDF (265 kB) Citations (8)
References:
Abstract: For every finite-dimensional nilpotent complex Lie algebra or superalgebra $\mathfrak n$, we offer three algorithms for realizing it in terms of creation and annihilation operators. We use these algorithms to realize Lie algebras with a maximal subalgebra of finite codimension. For a simple finite-dimensional $\mathfrak g$ whose maximal nilpotent subalgebra is $\mathfrak n$, this gives its realization in terms of first-order differential operators on the big open cell of the flag manifold corresponding to the negative roots of $\mathfrak g$. For several examples, we executed the algorithms using the MATHEMATICA-based package SUPERLie. These realizations form a preparatory step in an explicit construction and description of an interesting new class of simple Lie (super)algebras of polynomial growth, generalizations of the Lie algebra of matrices of complex size.
Received: 09.02.2000
English version:
Theoretical and Mathematical Physics, 2000, Volume 124, Issue 2, Pages 1048–1058
DOI: https://doi.org/10.1007/BF02551076
Bibliographic databases:
Language: Russian
Citation: Č. Burdík, P. Ya. Grozman, D. A. Leites, A. N. Sergeev, “Realization of Lie algebras and superalgebras in terms of creation and annihilation operators: I”, TMF, 124:2 (2000), 227–238; Theoret. and Math. Phys., 124:2 (2000), 1048–1058
Citation in format AMSBIB
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\paper Realization of Lie algebras and superalgebras in terms of creation and annihilation operators: I
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\issue 2
\pages 227--238
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\transl
\jour Theoret. and Math. Phys.
\yr 2000
\vol 124
\issue 2
\pages 1048--1058
\crossref{https://doi.org/10.1007/BF02551076}
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  • https://www.mathnet.ru/eng/tmf635
  • https://doi.org/10.4213/tmf635
  • https://www.mathnet.ru/eng/tmf/v124/i2/p227
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:547
    Full-text PDF :256
    References:69
    First page:1
     
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