Curved Casimir operators and the BGG machinery.

Čap, Andreas; Souček, Vladimír

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Prolongation of linear semibasic tangent valued forms to product preserving gauge bundles of vector bundles.

Wlodzimierz M. Mikulski (2006)

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Let A be a Weil algebra and V be an A-module with dim V < ∞. Let E → M be a vector bundle and let TE → TM be the vector bundle corresponding to (A,V). We construct canonically a linear semibasic tangent valued p-form Tφ : T E → ΛT*TM ⊗ TTE on TE → TM from a linear semibasic tangent valued p-form φ : E → ΛT*M ⊗ TE on E → M. For the Frolicher-Nijenhuis bracket we prove that [[Tφ, Tψ]] = T ([[φ,ψ]]) for any linear semibasic tangent valued p- and q-forms φ and ψ on E → M. We apply...

Representation of a gauge group as motions of a Hilbert space

Clara Lucía Aldana Domínguez (2004)

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This is a survey article based on the author’s Master thesis on affine representations of a gauge group. Most of the results presented here are well-known to differential geometers and physicists familiar with gauge theory. However, we hope this short systematic presentation offers a useful self-contained introduction to the subject. In the first part we present the construction of the group of motions of a Hilbert space and we explain the way in which it can be considered...

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Martin Čadek, Jiří Vanžura (1998)

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The paper is an overview of our results concerning the existence of various structures, especially complex and quaternionic, in 8-dimensional vector bundles over closed connected smooth 8-manifolds.