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.
New examples of Lie algebras with ad-invariant metrics found.
Study on uniqueness of ad-invariant metrics in Lie algebras.
This is a survey work on Lie algebras with ad-invariant metrics. We summarize main features, notions and constructions, in the aim of bringing into consideration the main research on the topic. We also give some list of examples in low dimensions.
In this work we study a particular class of Lie bialgebras arising from Hermitian structures on Lie algebras such that the metric is ad-invariant. We will refer to them as Lie bialgebras of complex type. These give rise to Poisson Lie groups G whose corresponding duals G* are complex Lie groups. We also prove that a He…
A family of naturally reductive pseudo-Riemannian spaces is constructed out of the representations of Lie algebras with ad-invariant metrics. We exhibit peculiar examples, study their geometry and characterize the corresponding naturally reductive homogeneous structure.
Integrates quadratic Lie algebroids to Riemannian Cartan-Lie groupoids.
Convexity proven for sums of angles of unitary paths.
The paper classifies metrics on a Heisenberg group's cotangent bundle.
Develops new Poisson structures for moduli spaces.
A variational principle connects fields to principal bundles and Einstein-Yang-Mills systems.
In the eighties Goldman discovered a Lie algebra structure on the vector space generated by the free homotopy classes of oriented curves on an oriented surface. The Lie bracket [a,b] is defined as the signed sum over the intersection points of a and b of the loop product of at the intersection points. If one of the cla…
The paper extends the classification of bi-invariant 2-forms to infinite-dimensional Lie groups.
Characterizes Lie groups with specific structures and finds a correspondence between carrollian and galilean Lie algebras.
We consider principal fibre bundles with a given connection and construct almost complex structures on the total space if the adjoint bundle is isomorphic to the tangent bundle of the base. We derive the integrability condition. If the structure group is compact, then a choice of an ad-invariant inner product on its Li…
Since the work of Henri Cartan finite dimensional Riemannian symmetric spaces are an important subject of mathematical interest. They are related in a natural way to semisimple Lie groups. In this work we introduce and study their infinite dimensional generalization: Affine Kac-Moody symmetric spaces. Affine Kac-Moody …
Classifies locally homogeneous connections on bundles over hyperbolic Riemann surfaces.