Thomas Strobl
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View article: Singular Riemannian foliations and $\mathcal{I}$-Poisson manifolds
Singular Riemannian foliations and $\mathcal{I}$-Poisson manifolds Open
We recall the notion of a singular foliation (SF) on a manifold M , viewed as an appropriate submodule of \mathfrak{X}(M) , and adapt it to the presence of a Riemannian metric g , yielding a module version of a singular Riemannian foliatio…
View article: Data on yield and soil parameters of three diverse tilled long-term experimental sites in Austria (2018–2022)
Data on yield and soil parameters of three diverse tilled long-term experimental sites in Austria (2018–2022) Open
The agroecological “Marchfeld” cluster assessed the impact of tillage on primary production (yield) and selected soil parameters at three sites (two conventionally and one organically managed) from 2018–2022. The data were uniformly compil…
View article: Principaloid bundles
Principaloid bundles Open
We present a novel generalisation of principal bundles -- principaloid bundles: These are fibre bundles $π:P\to B$ where the typical fibre is the arrow manifold $G$ of a Lie groupoid $G\rightrightarrows M$ and the structure group is reduce…
View article: The minimal Lie groupoid and infinity algebroid of the singular octonionic Hopf foliation
The minimal Lie groupoid and infinity algebroid of the singular octonionic Hopf foliation Open
The famous singular leaf decomposition $\mathcal{L}_{OH}$ of $\mathbb{R}^{16}\cong \mathbb{O}^2$ induced by the Hopf construction for octonions $\mathbb{O}$ has no known Lie group action generating it. In this article we construct a $\math…
View article: Koszul-Tate resolutions and decorated trees
Koszul-Tate resolutions and decorated trees Open
Given a commutative algebra $\mathcal O$, a proper ideal $\mathcal I$, and a resolution of $\mathcal O/ \mathcal I$ by projective $\mathcal O $-modules, we construct an explicit Koszul-Tate resolution. We call it the arborescent Koszul-Tat…
View article: BFV extensions for mechanical systems with Lie-2 symmetry
BFV extensions for mechanical systems with Lie-2 symmetry Open
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View article: Topological Dirac sigma models and the classical master equation
Topological Dirac sigma models and the classical master equation Open
We present the construction of the classical Batalin–Vilkovisky (BV) action for topological Dirac sigma models. The latter are two-dimensional topological field theories that simultaneously generalise the completely gauged Wess–Zumino–Novi…
View article: Singular Riemannian foliations and $\mathcal{I}$-Poisson manifolds
Singular Riemannian foliations and $\mathcal{I}$-Poisson manifolds Open
We recall the notion of a singular foliation (SF) on a manifold $M$, viewed as an appropriate submodule of $\mathfrak{X}(M)$, and adapt it to the presence of a Riemannian metric $g$, yielding a module version of a singular Riemannian folia…
View article: Topological Dirac Sigma Models and the Classical Master Equation
Topological Dirac Sigma Models and the Classical Master Equation Open
We present the construction of the classical Batalin-Vilkovisky action for topological Dirac sigma models. The latter are two-dimensional topological field theories that simultaneously generalise the completely gauged Wess-Zumino-Novikov-W…
View article: BFV extensions and their obstructions in mechanical systems with Lie-2 symmetry.
BFV extensions and their obstructions in mechanical systems with Lie-2 symmetry. Open
We study mechanical models with first class constraints, not restricting to only regular and irreducible ones. We show that while the BFV charge always exists, the BFV extension of the Hamiltonian may be obstructed. Somewhat astonishingly …
View article: BFV extensions for mechanical systems with Lie-2 symmetry
BFV extensions for mechanical systems with Lie-2 symmetry Open
We consider mechanical systems on $T^*M$ with possibly irregular and reducible first class contraints linear in the momenta, which thus correspond to singular foliations on $M$. According to a recent result, the latter ones have a Lie-infi…
View article: The Universal Lie $\infty$-Algebroid of a Singular Foliation
The Universal Lie $\infty$-Algebroid of a Singular Foliation Open
We consider singular foliations \mathcal{F} as locally finitely generated \mathscr{O} -submodules of \mathscr{O} -derivations closed under the Lie bracket, where \mathscr{O} is the ring of smooth, holomorphic, or real analytic functions on…
View article: Leibniz-Yang-Mills gauge theories and the 2-Higgs mechanism
Leibniz-Yang-Mills gauge theories and the 2-Higgs mechanism Open
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View article: Leibniz-Yang-Mills Gauge Theories
Leibniz-Yang-Mills Gauge Theories Open
A quadratic Leibniz algebra $(\mathbb{V},[ \cdot, \cdot ],\kappa)$ gives rise to a canonical Yang-Mills type functional $S$ over every space-time manifold. The gauge fields consist of 1-forms $A$ taking values in $\mathbb{V}$ and 2-forms $…
View article: Transverse generalized metrics and 2d sigma models
Transverse generalized metrics and 2d sigma models Open
We reformulate the compatibility condition between a generalized metric and a small (non-maximal rank) Dirac structure in an exact Courant algebroid found in the context of the gauging of strings and formulated by means of two connections …
View article: Lie algebroids, gauge theories, and compatible geometrical structures
Lie algebroids, gauge theories, and compatible geometrical structures Open
The construction of gauge theories beyond the realm of Lie groups and algebras leads one to consider Lie groupoids and algebroids equipped with additional geometrical structures which, for gauge invariance of the construction, need to sati…
View article: The universal Lie $\infty$-algebroid of a singular foliation
The universal Lie $\infty$-algebroid of a singular foliation Open
We associate a Lie $\infty$-algebroid to every resolution of a singular foliation, where we consider a singular foliation as a locally generated $\mathscr{O}$-submodule of vector fields on the underlying manifold closed under Lie bracket. …
View article: Strings in Singular Space-Times and their Universal Gauge Theory
Strings in Singular Space-Times and their Universal Gauge Theory Open
We study the propagation of bosonic strings in singular target space-times. For describing this, we assume this target space to be the quotient of a smooth manifold $M$ by a singular foliation ${\cal F}$ on it. Using the technical tool of …
View article: Non-Abelian gerbes and enhanced Leibniz algebras
Non-Abelian gerbes and enhanced Leibniz algebras Open
We present the most general gauge-invariant action functional for coupled 1- and 2-form gauge fields with kinetic terms in generic dimensions, i.e. dropping eventual contributions that can be added in particular space-time dimensions only …
View article: Geometry on Lie algebroids I: compatible geometric structures on the base
Geometry on Lie algebroids I: compatible geometric structures on the base Open
The object of our study is a Lie algebroid $A$ or a Cartan-Lie algebroid $(A,\nabla)$ (a Lie algebroid with a compatible connection) over a base manifold $M$ equipped with appropriately compatible geometrical structures. The main focus is …