The graded differential geometry of mixed symmetry tensors

DOI10.5817/AM2019-2-123zbMath1474.53289arXiv1806.04048OpenAlexW3103701461WikidataQ114013212 ScholiaQ114013212MaRDI QIDQ5227081

Eduardo Ibarguëngoytia, Andrew James Bruce

Publication date: 5 August 2019

Published in: Archivum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.04048

zbMATH Keywords

curved spacetimesdensity bundle\(\mathbb{Z}^n_2\)-manifoldsbi-complexbi-formsde Rham differentialsdual gravitonsmixed symmetry tensorsnon-homological vector fieldstwisted bi-forms

Mathematics Subject Classification ID

Differential geometric aspects in vector and tensor analysis (53A45) Applications of global differential geometry to the sciences (53C80) Supermanifolds and graded manifolds (58A50) Methods of noncommutative geometry in general relativity (83C65)

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Cites Work

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• Splitting theorem for \(\mathbb{Z}_2^n\)-supermanifolds
• Darboux theorem and equivariant Morse lemma
• Supersymmetric quantum mechanics and super-Lichnerowicz algebras
• Exotic tensor gauge theory and duality
• Tensor gauge fields in arbitrary representations of \(\operatorname{GL}(D,\mathbb R)\). Duality and Poincaré lemma
• Tensor fields of mixed Young symmetry type and \(N\)-complexes
• Dual double field theory
• Tensor Galileons and gravity
• \(Q\)-manifolds and Mackenzie theory
• Towards integration on colored supermanifolds
• The category of Z2n-supermanifolds
• Infinite-Dimensional and Colored Supermanifolds
• Strongly coupled gravity and duality

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