QUANTUM HAMILTONIAN REDUCTION AND WB ALGEBRA

1992 ◽  
Vol 07 (20) ◽  
pp. 4885-4898 ◽  
Author(s):  
KATSUSHI ITO
Keyword(s):  
Lie Algebras ◽  
Free Field ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Hamiltonian Reduction ◽  
Affine Lie Algebras ◽  
Quantum Hamiltonian Reduction ◽  
Free Field Realization ◽  
Coset Construction ◽  
Quantum Hamiltonian

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.

scholarly journals LIE SUPERALGEBRA AND EXTENDED TOPOLOGICAL CONFORMAL SYMMETRY IN NON-CRITICAL W3-STRINGS

1994 ◽  
Vol 09 (33) ◽  
pp. 3063-3075 ◽  
Author(s):  
KATSUSHI ITO ◽  
HIROAKI KANNO
Keyword(s):  
String Theory ◽  
Root System ◽  
Simple Root ◽  
Similarity Transformation ◽  
Conformal Symmetry ◽  
Free Field ◽  
Lie Superalgebra ◽  
Hamiltonian Reduction ◽  
Free Field Realization ◽  
Quantum Hamiltonian

We obtain a new free field realization of N = 2 super W3-algebra using the technique of quantum Hamiltonian reduction. The construction is based on a particular choice of the simple root system of the affine Lie superalgebra sl (3|2)(1) associated with a non-standard sl (2) embedding. After twisting and a similarity transformation, this W-algebra can be identified as the extended topological conformal algebra of non-critical W3 string theory.

scholarly journals HAMILTONIAN REDUCTION AND TOPOLOGICAL CONFORMAL ALGEBRA IN c<1 NON-CRITICAL STRINGS

1994 ◽  
Vol 09 (15) ◽  
pp. 1377-1388 ◽  
Author(s):  
KATSUSHI ITO ◽  
HIROAKI KANNO
Keyword(s):  
Topological Algebra ◽  
Free Field ◽  
Lie Superalgebra ◽  
Conformal Algebra ◽  
Hamiltonian Reduction ◽  
Quantum Case ◽  
Operator Formalism ◽  
Free Field Realization ◽  
Brst Cohomology ◽  
Lax Operator

We study the Hamiltonian reduction of affine Lie superalgebra sl(2|1)(1). Based on a scalar Lax operator formalism, we derive the free field realization of the classical topological algebra which appears in the c≤1 non-critical strings. In the quantum case, we analyze the BRST cohomology to get the quantum free field expression of the algebra.

THE SU(2)0 WZNW MODEL

2003 ◽  
Vol 18 (25) ◽  
pp. 4685-4702
Author(s):  
ALEXANDER NICHOLS
Keyword(s):  
Correlation Functions ◽  
Free Field ◽  
Hamiltonian Reduction ◽  
Close Correspondence ◽  
Quantum Hamiltonian Reduction ◽  
Quantum Hamiltonian ◽  
Wznw Model

We analyse the correlation functions and operator content of the SU(2)0 model using both the free field description and the solutions to the Knizhnik-Zamolodchikov equations. We show that there is a very close correspondence between this model and the well studied c=-2 theory. We also demonstrate that the quantum Hamiltonian reduction of SU(2)0 leads very directly to the correlation functions of the c=-2 model.

Some studies on central derivation of nilpotent Lie superalgebra

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.

Restricted Envelopes of Lie Superalgebras

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.

REMARKS ON THE BRST QUANTIZED GAUGED WZNW MODELS AND THE TODA FIELD THEORIES

1991 ◽  
Vol 06 (10) ◽  
pp. 885-891 ◽  
Author(s):  
NOBUHARU HAYASHI
Keyword(s):  
Coupling Constants ◽  
Field Theories ◽  
Hamiltonian Reduction ◽  
Quantum Hamiltonian Reduction ◽  
Quantum Hamiltonian

It is shown that the quantum Hamiltonian reduction proposed by Bershadsky and Ooguri enables us to connect the gauged WZNW models with fractional levels to the quantum Toda field theories, and the coupling constants of the Toda field theories with the fractional levels. The BRST framework is applied to the SL (n, ℝ)-WZNW models.

scholarly journals Quantization of Calogero-Painlevé System and Multi-Particle Quantum Painlevé Equations II-VI

2021 ◽  
Author(s):  
Fatane Mobasheramini ◽  
◽  
Marco Bertola ◽  
Keyword(s):  
Canonical Quantization ◽  
Classical Case ◽  
Particle Systems ◽  
Integral Representations ◽  
Painlevé Equations ◽  
Hamiltonian Reduction ◽  
Painleve Equations ◽  
Special Representation ◽  
Quantum Hamiltonian Reduction ◽  
Quantum Hamiltonian

We consider the isomonodromic formulation of the Calogero-Painlevé multi-particle systems and proceed to their canonical quantization. We then proceed to the quantum Hamiltonian reduction on a special representation to radial variables, in analogy with the classical case and also with the theory of quantum Calogero equations. This quantized version is compared to the generalization of a result of Nagoya on integral representations of certain solutions of the quantum Painlevé equations. We also provide multi-particle generalizations of these integral representations.

scholarly journals On the Cohomology and Extensions of n-ary Multiplicative Hom-Nambu-Lie Superalgebras

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Lijun Tian ◽  
Baoling Guan ◽  
Yao Ma
Keyword(s):  
Lie Algebras ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Finite Dimensional

In this paper, we discuss the representations of n-ary multiplicative Hom-Nambu-Lie superalgebras as a generalization of the notion of representations for n-ary multiplicative Hom-Nambu-Lie algebras. We also give the cohomology of an n-ary multiplicative Hom-Nambu-Lie superalgebra and obtain a relation between extensions of an n-ary multiplicative Hom-Nambu-Lie superalgebra b by an abelian one a and Z1b,a0¯. We also introduce the notion of T∗-extensions of n-ary multiplicative Hom-Nambu-Lie superalgebras and prove that every finite-dimensional nilpotent metric n-ary multiplicative Hom-Nambu-Lie superalgebra over an algebraically closed field of characteristic not 2 in the case α is a surjection is isometric to a suitable T∗-extension.

scholarly journals Localization of Free Field Realizations of Affine Lie Algebras

2015 ◽  
Vol 105 (4) ◽  
pp. 483-502 ◽  
Author(s):  
Vyacheslav Futorny ◽  
Dimitar Grantcharov ◽  
Renato A. Martins
Keyword(s):  
Lie Algebras ◽  
Free Field ◽  
Affine Lie Algebras
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