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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,742 papers · 148 categories

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← all fields·5 papers on “lie algebras” in Differential Geometry · 1 month

On the Dirac complement problemmath.SG

Study on the existence of Dirac complements for Dirac structures.

problem Existence of Dirac complements for Dirac structures.

method Cohomological techniques and Lie-theoretical methods.

result Non-existence of Dirac complements for certain Lie algebras.

Dirac structures Courant algebroids deformation theory cohomology Lie algebras

2026-07-16abs ↗pdf ↗

The Bernstein-Gelfand-Gelfand (BGG) Construction: Algebra, Geometry, and Analysis; Part Imath.DG

Lecture notes on BGG complexes using Lie groups and algebras.

problem Constructing BGG complexes on open domains.

method Representation theory of semisimple Lie groups and Lie algebras.

result Introduction of BGG complexes with Lie group and algebra insights.

BGG complexes Lie groups Lie algebras representation theory differential forms

2026-07-12abs ↗pdf ↗

Solvable Lie algebras obtained by quivers and Einstein metricsmath.DG

New Lie algebras from quivers lead to rigid Ricci solitons.

problem Constructing Lie algebras from quivers to study geometric structures.

method Using finite quivers without cycles to construct solvable Lie algebras and proving their geometric properties.

result Simply-connected Lie groups corresponding to these Lie algebras admit left-invariant Ricci solitons, and when quivers are oriented multi-trees, these groups are rigid.

Lie algebras quivers Ricci solitons geometric structures rigidity

2026-07-08abs ↗pdf ↗

The Spencer cohomology and integrability of multisymplectic structuresmath.DG

The study of multisymplectic structures using Spencer cohomology.

problem Integrability of multisymplectic structures.

method Applying Spencer cohomology to identify multisymplectic structures as

G

-structures and giving conditions for integrability.

result Conditions for a multisymplectic form to admit a chart with constant coefficients.

multisymplectic structures Spencer cohomology integrability Darboux theorem Lie algebras

2026-07-06abs ↗pdf ↗

Homogeneous Hypersurfaces in 4-dimensional Thurston Geometries with 4-dimensional Isometry Groupmath.DG

Classifies homogeneous hypersurfaces in specific 4D geometries.

problem Classifying homogeneous hypersurfaces in 4D Thurston geometries.

method Analyzing subalgebras of Lie algebras and isometry groups.

result Determined all homogeneous hypersurfaces up to ambient isometries.

homogeneous hypersurfaces Thurston geometries Lie algebras isometry groups subalgebras

2026-06-26abs ↗pdf ↗