Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics

We study the quantum Hamiltonian reduction of affine Lie algebras and the free field realization of the associated W algebra. For the nonsimply laced case this reduction does not agree with the usual coset construction of the W minimal model. In particular, we find that the coset model [Formula: see text] can be obtained through the quantum Hamiltonian reduction of the affine Lie superalgebra B(0, n)(1). To show this we also construct the Feigin-Fuchs representation of affine Lie superalgebras.

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Some studies on central derivation of nilpotent Lie superalgebra

Asian-European Journal of Mathematics ◽

10.1142/s1793557120500680 ◽

2018 ◽

Vol 13 (04) ◽

pp. 2050068

Author(s):

Rudra Narayan Padhan ◽

K. C. Pati

Keyword(s):

Lie Algebra ◽

Lie Algebras ◽

Lie Superalgebra ◽

Lie Superalgebras ◽

Nilpotent Lie Algebra ◽

New Concepts

Many theorems and formulas of Lie superalgebras run quite parallel to Lie algebras, sometimes giving interesting results. So it is quite natural to extend the new concepts of Lie algebra immediately to Lie superalgebra case as the later type of algebras have wide applications in physics and related theories. Using the concept of isoclinism, Saeedi and Sheikh-Mohseni [A characterization of stem algebras in terms of central derivations, Algebr. Represent. Theory 20 (2017) 1143–1150; On [Formula: see text]-derivations of Filippov algebra, to appear in Asian-Eur. J. Math.; S. Sheikh-Mohseni, F. Saeedi and M. Badrkhani Asl, On special subalgebras of derivations of Lie algebras, Asian-Eur. J. Math. 8(2) (2015) 1550032] recently studied the central derivation of nilpotent Lie algebra with nilindex 2. The purpose of the present paper is to continue and extend the investigation to obtain some similar results for Lie superalgebras, as isoclinism in Lie superalgebra is being recently introduced.

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Lie Algebras, Vertex Algebras, and Automorphic Forms

Progress in Mathematics - Developments and Trends in Infinite-Dimensional Lie Theory ◽

10.1007/978-0-8176-4741-4_5 ◽

2010 ◽

pp. 151-168 ◽

Cited By ~ 2

Author(s):

Nils R. Scheithauer

Keyword(s):

Lie Algebras ◽

Automorphic Forms ◽

Vertex Algebras

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Restricted Envelopes of Lie Superalgebras

Algebra Colloquium ◽

10.1142/s1005386715000279 ◽

2015 ◽

Vol 22 (02) ◽

pp. 309-320

Author(s):

Liping Sun ◽

Wende Liu ◽

Xiaocheng Gao ◽

Boying Wu

Keyword(s):

Lie Algebra ◽

Lie Algebras ◽

Lie Superalgebra ◽

Lie Superalgebras ◽

Cartan Type ◽

Modular Lie Algebras ◽

Modular Lie Superalgebras

Certain important results concerning p-envelopes of modular Lie algebras are generalized to the super-case. In particular, any p-envelope of the Lie algebra of a Lie superalgebra can be naturally extended to a restricted envelope of the Lie superalgebra. As an application, a theorem on the representations of Lie superalgebras is given, which is a super-version of Iwasawa's theorem in Lie algebra case. As an example, the minimal restricted envelopes are computed for three series of modular Lie superalgebras of Cartan type.

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