A global perspective to connections on principal 2-bundles
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Konrad Waldorf
Abstract
For a strict Lie 2-group, we develop a notion of Lie 2-algebra-valued differential forms on Lie groupoids, furnishing a differential graded-commutative Lie algebra equipped with an adjoint action of the Lie 2-group and a pullback operation along Morita equivalences between Lie groupoids. Using this notion, we define connections on principal 2-bundles as Lie 2-algebra-valued 1-forms on the total space Lie groupoid of the 2-bundle, satisfying a condition in complete analogy to connections on ordinary principal bundles. We carefully treat various notions of curvature, and prove a classification result by the non-abelian differential cohomology of Breen–Messing. This provides a consistent, global perspective to higher gauge theory.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: WA 3300/1-1
Funding statement: This work was supported by the German Research Foundation under project code WA 3300/1-1.
A Formulary for calculations in strict Lie 2-algebras
The formulas presented here are valid for a strict Lie 2-algebra consisting of Lie algebras
Formulas involving the adjoint action are
Formulas involving the map
Formulas involving the map
Formulas involving the exterior derivative are
References
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Distinct distances between points and lines in 𝔽q2
- A global perspective to connections on principal 2-bundles
- Integral group rings of solvable groups with trivial central units
- Lefschetz property and powers of linear forms in 𝕂[x,y,z]
- On quasi-convex null sequences in infinite cyclic groups
- On autocommutators and the autocommutator subgroup in infinite abelian groups
- Anticyclotomic p-ordinary Iwasawa theory of elliptic modular forms
- Finite-dimensional representations of Leavitt path algebras
- Orlicz dual affine quermassintegrals
- Universal locally finite maximally homogeneous semigroups and inverse semigroups
- Von Neumann algebras, L-algebras, Baer *-monoids, and Garside groups
- Boundedness and compactness of Hardy-type integral operators on Lorentz-type spaces
- A shifted convolution sum for \mathrm{GL}(3) × \mathrm{GL}(2)
- Equivariant Gauss sum of finite quadratic forms
- Right 2-Engel elements, central automorphisms and commuting automorphisms of Lie algebras
-
Solution of Brauer’s
Articles in the same Issue
- Frontmatter
- Distinct distances between points and lines in 𝔽q2
- A global perspective to connections on principal 2-bundles
- Integral group rings of solvable groups with trivial central units
- Lefschetz property and powers of linear forms in 𝕂[x,y,z]
- On quasi-convex null sequences in infinite cyclic groups
- On autocommutators and the autocommutator subgroup in infinite abelian groups
- Anticyclotomic p-ordinary Iwasawa theory of elliptic modular forms
- Finite-dimensional representations of Leavitt path algebras
- Orlicz dual affine quermassintegrals
- Universal locally finite maximally homogeneous semigroups and inverse semigroups
- Von Neumann algebras, L-algebras, Baer *-monoids, and Garside groups
- Boundedness and compactness of Hardy-type integral operators on Lorentz-type spaces
- A shifted convolution sum for \mathrm{GL}(3) × \mathrm{GL}(2)
- Equivariant Gauss sum of finite quadratic forms
- Right 2-Engel elements, central automorphisms and commuting automorphisms of Lie algebras
-
Solution of Brauer’s
