Search results for "Kac–Moody algebra"

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A class of nilpotent Lie algebras admitting a compact subgroup of automorphisms

2017

Abstract The realification of the ( 2 n + 1 ) -dimensional complex Heisenberg Lie algebra is a ( 4 n + 2 ) -dimensional real nilpotent Lie algebra with a 2-dimensional commutator ideal coinciding with the centre, and admitting the compact algebra sp ( n ) of derivations. We investigate, in general, whether a real nilpotent Lie algebra with 2-dimensional commutator ideal coinciding with the centre admits a compact Lie algebra of derivations. This also gives us the occasion to revisit a series of classic results, with the expressed aim of attracting the interest of a broader audience.

Discrete mathematicsPure mathematicsOscillator algebra010102 general mathematicsUniversal enveloping algebra010103 numerical & computational mathematics01 natural sciencesAffine Lie algebraLie conformal algebraGraded Lie algebraNilpotent Lie algebraComputational Theory and MathematicsLie algebraCompact Lie algebraSettore MAT/03 - GeometriaGeometry and Topology0101 mathematicsCompact derivationGeneralized Kac–Moody algebraAnalysisMathematicsDifferential Geometry and its Applications
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Simple and semisimple Lie algebras and codimension growth

1999

Discrete mathematicsAdjoint representation of a Lie algebraPure mathematicsRepresentation of a Lie groupApplied MathematicsGeneral MathematicsSimple Lie groupFundamental representationReal formKilling formKac–Moody algebraAffine Lie algebraMathematicsTransactions of the American Mathematical Society
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Star-products and phase space realizations of quantum groups

1992

It is shown for a family of *-products (i.e. different ordering rules) that, under a strong invariance condition, the functions of the quadratic preferred observables (which generate the Cartan subalgebra in phase space realization of Lie algebras) take only the linear or exponential form. An exception occurs for the case of a symmetric ordering *-product where trigonometric functions and two special polynomials can also be included. As an example, the ‘quantized algebra’ of the oscillator Lie algebra is argued.

AlgebraPure mathematicsSubalgebraCartan matrixCartan subalgebraReal formStatistical and Nonlinear PhysicsKilling formKac–Moody algebraMathematical PhysicsMathematicsLie conformal algebraGraded Lie algebraLetters in Mathematical Physics
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