Leibniz cohomology for differentiable manifolds

Lodder, Jerry

doi:10.5802/aif.1611

Cited by 33 publications

(31 citation statements)

References 10 publications

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“…If all the (co)homology theory and the identification of the symplectic spaces remains the same in analog, then the picture for the demisemidirect product of V with p would be complete. Although specific examples have been worked out, there is as yet no general theory that will do the trick although there has been some progress [7,8]. This is a point at which we will just say that it is under consideration.…”

Section: (Co)homologymentioning

confidence: 94%

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The Poincaré Group in a Demisemidirect Product with a Non-associative Algebra with Representations that Include Particles and Quarks—II

Schroeck

2009

Int J Theor Phys

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The quarks and particles' mass and mass/spin relations are provided with coordinates in configuration space and/or momentum space by means of the marriage of ordinary Poincaré group representations with a non-associative algebra made through a demisemidirect product, in the notation of Leibniz algebras. Thus, we circumvent the restriction that the Poincaré group cannot be extended to a larger group by any means (including the (semi)direct product) to get even the mass relations. Finally, we will discuss a connection between the phase space representations of the Poincaré group and the phase space representations of the associated Leibniz algebra.

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Section: (Co)homologymentioning

confidence: 94%

“…Dixon [2], and the work by J-L. Loday and T. Pirashvili [7] and J.M. Lodder [8] on Leibniz algebras and cohomology has provided the input for a resolution of this interplay between what is a (not necessarily product associative) linear vector space property and the properties of the Poincaré group.…”

Section: Introductionmentioning

confidence: 99%

The Poincaré Group in a Demisemidirect Product with a Non-associative Algebra with Representations that Include Particles and Quarks—II

Schroeck

2009

Int J Theor Phys

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“…The filtration for the Pirashvili spectral sequence [9] [11] can be immediately applied to yield a decreasing filtration {F s * } s≥0 for C * RG (g) [2]. We use the same grading as in [9] [11], which becomes F 0 * = C * RG [2], and for s ≥ 1,…”

Section: Leibniz Cohomologymentioning

confidence: 99%

Rigidity of secondary characteristic classes

Lodder

2000

Differential Geometry and its Applications

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“…We will recall this cohomology in the next section for the deformation of Courant pairs. We know that the Leibniz algebra cohomology space HL * (χ( n ).) and the Lie algebra cohomology space H * (χ( n ),) are different as there are new generators for the dual Leibniz algebra structure over the Leibniz cohomology space [27,28].…”

Section: →Cmentioning

confidence: 99%