Related papers: Affine structures on Lie groupoids

A linear Gr-category is a category of finite-dimensional vector spaces graded by a finite group together with natural tensor product. We classify the braided monoidal structures of a class of linear Gr-categories via explicit computations…

This paper deals with affine connections on real manifolds. We give a new characterization of flat affine connections on real manifolds by means of certain affine representations of the Lie group of automorphisms preserving the connection.…

We construct rank 2 thick nondiscrete affine buildings associated with an arbitrary finite dihedral group.

We study algebraic and geometric properties of metric spaces endowed with dilatation structures, which are emergent during the passage through smaller and smaller scales. In the limit we obtain a generalization of metric affine geometry,…

We prove that any real Lie group of dimension \leq 5 admits a left invariant flat projective structure. We also prove that a real Lie group L of dimension \leq 5 admits a left invariant flat affine structure if and only if the Lie algebra…

We first recall two equivalent definitions of Lie $2$-algebras, categorification of Lie algebras and $2$-term $L_\infty$-algebras. Then we present four different kinds of Lie $2$-algebras from $2$-plectic manifolds, Courant algebroids,…

Given a positive definite even lattice and a commutative ring, there is a standard construction of a lattice vertex algebra over the commutative ring, and it admits a natural grading by non-negative integers. We describe the groups of…

A branched affine structure on a compact topological surface with marked points is a complex affine structure outside the marked points. We give a proof of an unpublished foundational theorem of Veech, stating that any branched affine…

We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically…

We interpret and develop a theory of loop algebras as torsors (principal homogeneous spaces) over Laurent polynomial rings . As an application, we recover Kac's realization of affine Kac-Moody Lie algebras.

We construct a category of flat vector bundles on an elliptic curve. It arises in the representation theory of quantum affine algebras and carries meromorphic braided structure with singularities on the diagonal of the square of the curve.

We classify the 6-dimensional Lie algebras that can be endowed with an abelian complex structure and parameterize, on each of these algebras, the space of such structures up to holomorphic isomorphism.

We investigate the existence of $p$-K\"ahler structures on two classes of complex manifolds: on quasi-regular fibrations, with particular emphasis on complex homogeneous spaces, and on reductive Lie groups endowed with invariant complex…

We present a new application of affine Lie algebras to massive quantum field theory in 2 dimensions, by investigating the $q\to 1$ limit of the q-deformed affine $\hat{sl(2)}$ symmetry of the sine-Gordon theory, this limit occurring at the…

A group code structure of a linear code is a description of the code as one-sided or two-sided ideal of a group algebra of a finite group. In these realizations, the group algebra is identified with the ambient space, and the group elements…

We develop some foundations of commutative algebra, with a view towards algebraic geometry, in symmetric tensor categories. Most results establish analogues of classical theorems, in tensor categories which admit a tensor functor to some…

Poisson-NIjenhuis structures for an arbitrary Lie agebroid are defined and studied by means of tangent lifts of tensor fields.

We show how one can associate to a given class of finite type G-structures a classifying Lie algebroid. The corresponding Lie groupoid gives models for the different geometries that one can find in the class, and encodes also the different…

For any convex preorder on the set of positive roots of affine type A, we classify and construct all associated cuspidal and semicuspidal skew shapes. These combinatorial objects correspond to cuspidal and semicuspidal skew Specht modules…

We introduce affine structures on groups and show they form a category equivalent to that of semi-braces. In particular, such a new description of semi-braces includes that presented by Rump for braces. By specific affine structures, we…