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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
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
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
Linking options:
https://www.mathnet.ru/eng/tmf635https://doi.org/10.4213/tmf635 https://www.mathnet.ru/eng/tmf/v124/i2/p227
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Abstract page: | 547 | Full-text PDF : | 256 | References: | 69 | First page: | 1 |
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