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Let $L_{n} = K [x_{1}^{\pm 1}, ..., x_{n}^{\pm 1}]$ be a Laurent polynomial algebra over a field $K$ of characteristic zero, $W_{n} : = {Der}_{K} (L_{n})$ the Lie algebra of $K$ -derivations of the algebra $L_{n}$ , the so-called Witt Lie algebra, and let $Vir$ be the Virasoro Lie algebra which is a $1$ -dimensional central extension of the Witt Lie algebra. The Lie algebras $W_{n}$ and $Vir$ are infinite dimensional Lie algebras. We prove that the following isomorphisms of the groups of Lie algebra automorphisms hold: ${Aut}_{Lie} (Vir) ≃ {Aut}_{Lie} (W_{1}) ≃ {\pm 1} ⋉ K^{*}$ , and give a short proof that ${Aut}_{Lie} (W_{n}) ≃ {Aut}_{K - alg} (L_{n}) ≃ {GL}_{n} (ℤ) ⋉ K^{* n}$ .

The Kontsevich integral and quantized Lie superalgebras.

Geer, Nathan (2005)

Algebraic & Geometric Topology

The Lie algebra of endomorphisms of an infinite-dimensional vector space

Ian Stewart (1972)

Compositio Mathematica

The Minimal Condition for Subideals of Lie Algebras.

I.N. Stewart (1969)

Mathematische Zeitschrift

The structure of standard modules, I: Universal algebras and the Rogers-Ramanujan identities.

James Lepowsky, Robert L. Wilson (1984)

Inventiones mathematicae

The structure of standard modules. II. The case A1(1), principal gradation.

James Lepowsky, Robert Lee Wilson (1985)

Inventiones mathematicae

The supports of simple modules over toroidal algebras.

Mazorchuk, Volodymyr (1999)

Journal of Lie Theory

The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI

Henrik Aratyn, Johan van de LEUR (2005)

Annales de l’institut Fourier

Equivalence is established between a special class of Painlevé VI equations parametrized by a conformal dimension $μ$ , time dependent Euler top equations, isomonodromic deformations and three-dimensional Frobenius manifolds. The isomonodromic tau function and solutions of the Euler top equations are explicitly constructed in terms of Wronskian solutions of the 2-vector 1-constrained symplectic Kadomtsev-Petviashvili (CKP) hierarchy by means of Grassmannian formulation. These Wronskian solutions give...

Currently displaying 1 – 19 of 19

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Displaying 1 – 19 of 19

The algebra of compact operators does not have any finite-codimensional ideal

The arithmetic theory of loop groups

The automorphisms of generalized Witt type Lie algebras.

The derived join theorem and coalescence in Lie algebras

The Differentiable Structure of Three Remarkable Diffeomorphism Groups.

The groups of automorphisms of the Witt $W_{n}$ and Virasoro Lie algebras

The Kontsevich integral and quantized Lie superalgebras.

The Lie algebra of endomorphisms of an infinite-dimensional vector space

The Minimal Condition for Subideals of Lie Algebras.

The structure of standard modules, I: Universal algebras and the Rogers-Ramanujan identities.

The structure of standard modules. II. The case A1(1), principal gradation.

The supports of simple modules over toroidal algebras.

The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI

Théorie directe des groupes de Lie, I

Théorie directe des groupes de Lie, II

Théorie directe des groupes de Lie, III

Théorie directe des groupes de Lie, IV

Transformation de Mellin et algèbres de Kac-Moody

Transformation de Mellin, et algèbres de Mellin-Lie

Currently displaying 1 – 19 of 19