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Quasifinite highest weight modules over the Lie algebra of differential operators on the circle

AbstractWe classify positive energy representations with finite degeneracies of the Lie algebraW1+∞ and construct them in terms of representation theory of the Lie algebra
$$\hat gl(\infty ,R_m )$$
… Expand

Representation theory of the vertex algebraW1+∞

In our paper [KR] we began a systematic study of representations of the universal central extension of the Lie algebra of differential operators on the circle. This study was continued in the paper… Expand

W_1+∞ and W(gl_N) with central charge N

- E. Frenkel, V. Kac, A. Radul, W. Wang
- Mathematics
- 20 May 1994

The Lie algebra D̂, which is the unique non-trivial central extension of the Lie algebra D of differential operators on the circle [KP1], has appeared recently in various models of two-dimensional… Expand

Non-trivial central extensions of Lie algebras of differential operators in two and higher dimensions

- A. Radul
- Mathematics
- 8 August 1991

A family of poisson structures on hermitian symmetric spaces

- S. Khoroshkin, A. Radul, V. Rubtsov
- Mathematics
- 1 March 1993

We investigate the compatibility of symplectic Kirillov-Kostant-Souriau structure and Poisson-Lie structure on coadjoint orbits of semisimple Lie group. We prove that they are compatible for an orbit… Expand

W_{1+\infty} and W(gl_N) with central charge N

- E. Frenkel, V. Kac, A. Radul, W. Wang
- Mathematics
- 18 May 1994

We study representations of the central extension of the Lie algebra of differential operators on the circle, the W-infinity algebra. We obtain complete and specialized character formulas for a large… Expand

Representation theory of the vertex algebra $W_{1 + \infty}$

In our paper~\cite{KR} we began a systematic study of representations of the universal central extension $\widehat{\Cal D}\/$ of the Lie algebra of differential operators on the circle. This study… Expand

Noncommutative differential geometry related to the Young-Baxter equation

- D. Gurevich, A. Radul, V. Rubtsov
- Mathematics, Physics
- 10 November 1995

An analogue of the differential calculus associated with a unitary solution of the quantum Young-Baxter equation is constructed. An example of a ring sheaf is considered in which local solutions of… Expand

Generalized internal long waves equations: Construction, Hamiltonian structure, and conservation laws

- D. Lebedev, A. Radul
- Mathematics
- 1 December 1983

A general class of the ILW type equations is constructed. We introduce a Hamiltonian structure and construct an infinite number of conservation laws.

Poisson Structure for Restricted Lie Algebras

The Poisson bracket is an important invariant of a deformation of a commutative associative algebra A (cf. [D]). Given a family of associative (but not necessarily commutative) algebras Ah, such that… Expand

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