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Open AccessThe Controlling \(L_\infty \) -Algebra, Cohomology and Homotopy of Embedding Tensors and Lie–Leibniz Triples
In this paper, we first construct the controlling algebras of embedding tensors and Lie–Leibniz triples, which turn out to be a graded Lie algebra and an ...
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Article
Chern–Simons, Wess–Zumino and other cocycles from Kashiwara–Vergne and associators
Descent equations play an important role in the theory of characteristic classes and find applications in theoretical physics, e.g., in the Chern–Simons field theory and in the theory of anomalies. The second Che...
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Lie 2-Bialgebras
In this paper, we study Lie 2-bialgebras, paying special attention to coboundary ones, with the help of the cohomology theory of L ∞-algebras with coefficients in L ∞-modules. We c...
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Article
Open AccessIntegration of Lie 2-Algebras and Their Morphisms
Given a strict Lie 2-algebra, we can integrate it to a strict Lie 2-group by integrating the corresponding Lie algebra crossed module. On the other hand, the integration procedure of Getzler and Henriques will...
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Article
Open AccessNon-Hausdorff symmetries of C*-algebras
Symmetry groups or groupoids of C*-algebras associated to non-Hausdorff spaces are often non-Hausdorff as well. We describe such symmetries using crossed modules of groupoids. We define actions of crossed modu...
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Article
Open AccessKan Replacement of Simplicial Manifolds
We establish a functor Kan from local Kan simplicial manifolds to weak Kan simplicial manifolds. It gives a solution to the problem of extending local Lie groupoids to Lie 2-groupoids.
