Splitting theorem for \(\mathbb{Z}_2^n\)-supermanifolds

DOI10.1016/j.geomphys.2016.09.006zbMath1404.58011arXiv1602.03671OpenAlexW2260471833MaRDI QIDQ335850

Tiffany Covolo, Norbert Poncin, Janusz Grabowski

Publication date: 2 November 2016

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.03671

zbMATH Keywords

supersymmetrysupergeometryhigher gradinghigher vector bundlesign rulesplit supermanifold

Mathematics Subject Classification ID

Supermanifolds and graded manifolds (58A50) Formal power series rings (13F25)

Related Items (24)

Irreducible representations of Z22-graded N=2 supersymmetry algebra and Z22-graded supermechanics ⋮ On the construction of \(\mathbb{Z}^n_2\)-Grassmannians as homogeneous \(\mathbb{Z}^n_2\)-spaces ⋮ Supersymmetrization: AKSZ and beyond? ⋮ The category of Z2n-supermanifolds ⋮ Polarisation of graded bundles ⋮ Integration on minimal Z22 -superspace and emergence of space ⋮ Extension of local positive definite \(\mathbb{Z}_2^n\)-superfunctions ⋮ \(\mathbb{Z}_2\times\mathbb{Z}_2\)-generalizations of infinite-dimensional Lie superalgebra of conformal type with complete classification of central extensions ⋮ Unnamed Item ⋮ Double-graded supersymmetric quantum mechanics ⋮ Double-graded quantum superplane ⋮ Z 2 n -graded extensions of supersymmetric quantum mechanics via Clifford algebras ⋮ The Gelfand–Naimark–Segal construction for unitary representations of $\mathbb Z_2^n$-graded Lie supergroups ⋮ Linear \(\mathbb{Z}_2^n\)-manifolds and linear actions ⋮ Products in the category of 𝕑2n-manifolds ⋮ The Schwarz-Voronov embedding of \(\mathbb{Z}_2^n\)-manifolds ⋮ Local forms of morphisms of colored supermanifolds ⋮ A classification of lowest weight irreducible modules over Z22-graded extension of osp(1|2) ⋮ The graded differential geometry of mixed symmetry tensors ⋮ Symplectic \(\mathbb{Z}_2^n\)-manifolds ⋮ Comments of \(\mathbb{Z}_2^2\)-supersymmetry in superfield formalism ⋮ On a \(\mathbb Z_2^n\)-graded version of supersymmetry ⋮ Monoidally graded manifolds ⋮ ${\mathcal N}$ -extension of double-graded supersymmetric and superconformal quantum mechanics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The supergeometry of Loday algebroids
• On the category of Lie \(n\)-algebroids
• Higher trace and Berezinian of matrices over a Clifford algebra
• Higher vector bundles and multi-graded symplectic manifolds
• A new kind of graded Lie algebra and parastatistical supersymmetry
• Spinor-vector duality in heterotic string orbifolds
• Mathematical foundations of supersymmetry
• Towards integration on colored supermanifolds
• The Structure of Supermanifolds
• The category of Z2n-supermanifolds
• Two Approaches to Supermanifolds
• INTRODUCTION TO THE THEORY OF SUPERMANIFOLDS
• On Holomorphic Graded Manifolds
• Lie superalgebras of differential operators

This page was built for publication: Splitting theorem for \(\mathbb{Z}_2^n\)-supermanifolds