-(bi)derivations and transposed Poisson algebra structures on Lie algebras

A method of relating infinite dimensional Lie algebras to basis dependent sequences of finite dimensional Lie algebras is introduced. Diff A S2 and Diff A T2 are shown to be N → ∞ limits of SU(N), with a limiting procedure, and " SU (∞)'s", that differ from the usual Kac Moody ones. After a detailed presentation of these two 'principal' examples, the general construction is outlined, which seems to work for the Poisson algebra of more or less any homogenous symplectic manifold.

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VERTEX ALGEBRAS AND VERTEX POISSON ALGEBRAS

Communications in Contemporary Mathematics ◽

10.1142/s0219199704001264 ◽

2004 ◽

Vol 06 (01) ◽

pp. 61-110 ◽

Cited By ~ 37

Author(s):

HAISHENG LI

Keyword(s):

Vector Space ◽

Lie Algebras ◽

Poisson Algebra ◽

Vertex Algebra ◽

General Construction ◽

Vertex Algebras ◽

Poisson Algebras ◽

Formal Deformation ◽

Good Filtration

This paper studies certain relations among vertex algebras, vertex Lie algebras and vertex Poisson algebras. In this paper, the notions of vertex Lie algebra (conformal algebra) and vertex Poisson algebra are revisited and certain general construction theorems of vertex Poisson algebras are given. A notion of filtered vertex algebra is formulated in terms of a notion of good filtration and it is proved that the associated graded vector space of a filtered vertex algebra is naturally a vertex Poisson algebra. For any vertex algebra V, a general construction and a classification of good filtrations are given. To each ℕ-graded vertex algebra V=∐n∈ℕV(n) with [Formula: see text], a canonical (good) filtration is associated and certain results about generating subspaces of certain types of V are also obtained. Furthermore, a notion of formal deformation of a vertex (Poisson) algebra is formulated and a formal deformation of vertex Poisson algebras associated with vertex Lie algebras is constructed.

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Lie Groups, Lie Algebras, Cohomology and some Applications in Physics

10.1017/cbo9780511599897 ◽

1995 ◽

Cited By ~ 90

Author(s):

Josi A. de Azcárraga ◽

Josi M. Izquierdo

Keyword(s):

Lie Groups ◽

Lie Algebras

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The rigidity of some solvable Lie algebras

Uzbek Mathematical Journal ◽

10.29229/uzmj.2018-2-4 ◽

2018 ◽

Vol 2018 (2) ◽

pp. 43-49

Author(s):

R.K. Gaybullaev ◽

Kh.A. Khalkulova ◽

J.Q. Adashev

Keyword(s):

Lie Algebras ◽

Solvable Lie Algebras

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Integrable two-dimensional dynamical systems and the characteristic Lie algebras

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2007.1.023 ◽

2007 ◽

Vol 5 ◽

pp. 195-200

Author(s):

A.V. Zhiber ◽

O.S. Kostrigina

Keyword(s):

Dynamical System ◽

Dynamical Systems ◽

Lie Algebra ◽

Lie Algebras ◽

Second Order ◽

System Of Equations ◽

Two Dimensional ◽

Finite Dimensional ◽

Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

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Reduction of partially invariant submodels of rank 3 defect 1 to invariant submodels

Multiphase Systems ◽

10.21662/mfs2018.3.009 ◽

2018 ◽

Vol 13 (3) ◽

pp. 59-63 ◽

Cited By ~ 1

Author(s):

D.T. Siraeva

Keyword(s):

Equation Of State ◽

Lie Algebra ◽

Lie Algebras ◽

Gas Dynamics ◽

Hydrodynamic Type ◽

System Of Equations ◽

Two Dimensional ◽

Equations Of Gas Dynamics ◽

Entropy Functions

Equations of hydrodynamic type with the equation of state in the form of pressure separated into a sum of density and entropy functions are considered. Such a system of equations admits a twelve-dimensional Lie algebra. In the case of the equation of state of the general form, the equations of gas dynamics admit an eleven-dimensional Lie algebra. For both Lie algebras the optimal systems of non-similar subalgebras are constructed. In this paper two partially invariant submodels of rank 3 defect 1 are constructed for two-dimensional subalgebras of the twelve-dimensional Lie algebra. The reduction of the constructed submodels to invariant submodels of eleven-dimensional and twelve-dimensional Lie algebras is proved.

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