Search results for "Infinitesimal deformation"

showing 2 items of 2 documents

About Leibniz cohomology and deformations of Lie algebras

2011

We compare the second adjoint and trivial Leibniz cohomology spaces of a Lie algebra to the usual ones by a very elementary approach. The comparison gives some conditions, which are easy to verify for a given Lie algebra, for deciding whether it has more Leibniz deformations than just the Lie ones. We also give the complete description of a Leibniz (and Lie) versal deformation of the 4-dimensional diamond Lie algebra, and study the case of its 5-dimensional analogue.

Leibniz algebraPure mathematicsAlgebra and Number TheoryMathematics::Rings and AlgebrasInfinitesimal deformationK-Theory and Homology (math.KT)17A32 17B56 14D15CohomologyMathematics::K-Theory and HomologyLie algebraMathematics - Quantum AlgebraMathematics - K-Theory and HomologyFOS: MathematicsQuantum Algebra (math.QA)Mathematics
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Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed

2015

We prove that the bihamiltonian cohomology of a semisimple pencil of Poisson brackets of hydrodynamic type vanishes for almost all degrees. This implies the existence of a full dispersive deformation of a semisimple bihamiltonian structure of hydrodynamic type starting from any infinitesimal deformation.

Mathematics - Differential GeometryFOS: Physical sciencesPoisson distribution01 natural sciencessymbols.namesakePoisson bracketMathematics::Quantum Algebra0103 physical sciencesFOS: Mathematics0101 mathematicsMathematics::Representation TheoryMathematics::Symplectic GeometryMathematical PhysicsPencil (mathematics)MathematicsAlgebra and Number TheoryNonlinear Sciences - Exactly Solvable and Integrable Systems010102 general mathematicsMathematical analysisInfinitesimal deformationMathematical Physics (math-ph)Cohomology[ MATH.MATH-DG ] Mathematics [math]/Differential Geometry [math.DG]Nonlinear Sciences::Exactly Solvable and Integrable SystemsDifferential Geometry (math.DG)[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]symbols010307 mathematical physicsGeometry and TopologyExactly Solvable and Integrable Systems (nlin.SI)Analysis
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