Central extensions of infinite-dimensional Lie algebras and Lie groups, Virasoro algebra and generalizations

DOI10.1016/0034-4877(96)89288-3zbMath0892.17018OpenAlexW2065619479MaRDI QIDQ1372441

Claude Roger

Publication date: 12 January 1998

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0034-4877(96)89288-3

zbMATH Keywords

surveyRiemann surfacescohomologyKac-Moody algebrascyclic homologyVirasoro algebraVirasoro groupLie algebra of vector fieldsgroups of diffeomorphismscurrent algebrasHamiltonian vector fieldscentral extensioncontact vector fieldsunimodular vector fieldsalgebras of meromorphic vector fields

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Virasoro and related algebras (17B68) Lie algebras of vector fields and related (super) algebras (17B66) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Graded Lie (super)algebras (17B70) Cohomology of Lie (super)algebras (17B56)

Related Items

Invariant Forms on Lie Algebra Extensions, On the Hamiltonian and geometric structure of Langmuir circulation, Central extensions of semidirect products and geodesic equations, Coadjoint orbits of vortex sheets in ideal fluids, Double extensions of Lie algebras of Kac-Moody type and applications to some Hamiltonian systems, Dual pairs in fluid dynamics, The path group construction of Lie group extensions, The Virasoro group and Lorentzian surfaces: The hyperboloid of one sheet, The \(L_\infty \)-algebra of a symplectic manifold, Geodesics on extensions of Lie groups and stability: The superconductivity equation, Towards a Lie theory of locally convex groups, Cocycles and stream functions in quasigeostrophic motion, Rotation number, geometrical structures on a circle and Bott-Virasoro group, Abstract Kelvin-Noether theorems for Lie group extensions, A two-dimensional analogue of the Virasoro algebra, Central extensions of infinite-dimensional Lie groups

Cites Work

• Extensions and contractions of the Lie algebra of \(q\)-pseudodifferential symbols on the circle
• Cyclic homology and the Lie algebra homology of matrices
• Application of the cohomology of graded Lie algebras to formal deformations of Lie algebras
• Coadjoint orbits of the Virasoro group
• Cyclic homology of differential operators
• 2-cocycles on the algebra of differential operators
• Cohomology of the Lie algebra of smooth vector fields of a manifold, associated to the Lie derivative of smooth forms
• Unitary representations of some infinite dimensional groups
• Cohomology of infinite-dimensional Lie algebras and characteristic classes of foliations
• Cyclic homology of differential operators, the Virasoro algebra and a \(q\)-analogue
• Invariants of the Euler equations for ideal or barotropic hydrodynamics and superconductivity in \(D\) dimensions
• Symplectic structures of the spaces of projective and affine curves
• Spin and wedge representations of infinite-dimensional Lie algebras and groups
• Lie superalgebras
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