For a Lie groupoid G we prove an analogous of the Baker-Campbell-Hausdorff formula and we calculate the structure functions of the Lie algebroid associated to G.
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7 results for “Baker--Campbell--Hausdorff”
The Baker-Campbell-Hausdorff formula and the Zassenhaus formula in synthetic differential geometrymath.DG
After the torch of Anders Kock [Taylor series calculus for ring objects of line type, Journal of Pure and Applied Algebra, 12 (1978), 271-293], we will establish the Baker-Campbell-Hausdorff formula as well as the Zassenhaus formula in the theory of Lie groups.
Explicit BCH series radii found for special Banach-Malcev shift algebras.
problem Finding convergence radii for BCH series in specific algebraic structures.
method Established explicit convergence radii using continuity estimates and algebraic properties.
result Explicit formula for convergence radii derived and validated for various shift algebras.
The notion of a symplectic expansion directly relates the topology of a surface to formal symplectic geometry. We give a method to construct a symplectic expansion by solving a recurrence formula given in terms of the Baker-Campbell-Hausdorff series.
Paper generalizes connections between Lie groups and affine connections.
problem Exploring properties of infinitesimal groups and affine connections.
method Introducing second-order infinitesimal groups and using them to define Lie brackets and connections.
result Generalized correspondence between symmetric and non-symmetric affine connections.
In this paper we establish the basic tools to develop the "Calculus" associated with group-valued continuously Pansu differentiable mappings. We develop the technical machinery on which all of our results rely. In particular, the linearization of addends appearing in the Baker-Campbell-Hausdorff formula is one of the m…
This work explores algebraic structures from curvature and torsion in affine connections.
problem Understanding algebraic structures from curvature and torsion in affine connections.
method Post-Lie algebra, D-algebra, and special polynomials.
result A particular class of geometrically special polynomials is generated by torsion and curvature.