Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2505.01350

Para-associative Algebroids

Andrew James Bruce
View original source ↗Read source document ↗Export metadata ↓

Abstract

We introduce para-associative algebroids as vector bundles whose sections form a ternary algebra with a generalised form of associativity. We show that a necessary and sufficient condition for local triviality is the existence of a differential connection, i.e., a connection that satisfies the Leibniz rule over the ternary product.

Explore related subjects

math.DGmath-phmath.MP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Andrew James Bruce. 2025-05-02. Para-associative Algebroids. https://doi.org/10.3390/math13142237

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Dirac operators twisted by ramified Euclidean line bundles

This article is concerned with the analysis of Dirac operators $D$ twisted by ramified Euclidean line bundles $(Z,\mathfrak{l})$-motivated by their relation with harmonic $\mathbf{Z}/2\mathbf{Z}$ spinors, which have appeared in various context in gauge theory and calibrated geometry. The closed extensions of $D$ are described in terms of the Gelfand-Robbin quotient $\check{\mathbf{H}}$. Assuming that the branching locus $Z$ is a closed cooriented codimension two submanifold, a geometric realisation of $\check{\mathbf{H}}$ is constructed. This, in turn, leads to an $L^2$ regularity theory.

math.DG↗
arXiv2026

New Solutions to the $G_2$ Hull-Strominger System via torus fibrations over $K3$ orbifolds

Using torus fibrations over K3 orbisurfaces, we construct new smooth solutions to the $G_2$ Hull-Strominger system. These manifolds arise as total spaces of principal $T^3$ (orbi)bundles over singular K3 surfaces. Our construction is based on the choice of three divisors on a singular K3 surface that are primitive with respect to a particular Kählermetric. The stable bundle is obtained via an adaptation of the Serre construction to the singular setting.

math.DG↗
arXiv2026

On vector-valued multisymplectic forms

We obtain a standard local presentation for a vector-valued multisymplectic form on a smooth manifold, generalizing the known proof for polysymplectic forms. We show that vector-valued multisymplectic forms on a finite-dimensional real vector space form a non-unital operad. We prove an entropy inequality for partial compositions.

math.DG↗