Related papers: Morphisms of generalized affine buildings
In this study, we try to generalize Bruhat-Tits's theory to the case of a Kac-Moody group, that is to define an affine building for a Kac-Moody group over a local field. Actually, we will obtain a geometric space wich lacks some of the…
We abstract Morimoto's construction of complex structures on product manifolds to pairs of certain generalized $F$-structures on manifolds that are not necessarily global products. As applications we characterize invariant generalized…
We are interested in abstract conditions that characterize homomorphic images of affine quandles. Our main result is a two-fold characterization of this class: one by a property of the displacement group, the other one by a property of the…
We construct (in significant generality) moduli spaces representing the functor of morphisms from a scheme into a solvable algebraic group.
Given an abelian category and a stability condition satisfying appropriate conditions, we define generalized $K$-theoretic invariants and prove that they satisfy wall-crossing formulas. For this, we introduce a new associative algebra…
We complete the foundational architecture of Algebraic Phase Theory by developing a categorical and $2$-categorical framework for algebraic phases. Building on the structural notions introduced in Papers~I-III, we define phase morphisms,…
We introduce a general theory of parametrized objects in the setting of infinity categories. Although spaces and spectra parametrized over spaces are the most familiar examples, we establish our theory in the generality of objects of a…
We introduce a universe of regular datatypes with variable binding information, for which we define generic formation and elimination (i.e. induction /recursion) operators. We then define a generic alpha-equivalence relation over the types…
We provide a treatment of isomorphism within a set-theoretic formulation of dependent type theory. Type expressions are assigned their natural set-theoretic compositional meaning. Types are divided into small and large types --- sets and…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
Automorphism groups are intrincate conjugacy invariants for subshifts, which can reveal important features of the dynamical structure of a shift action. One important case is the study of automorphism groups when the underlying subshift has…
We introduce the notion of a Lie algebroid structure on an affine bundle whose base manifold is fibred over the real numbers. It is argued that this is the framework which one needs for coming to a time-dependent generalization of the…
We establish the deformation theory of Lie groupoid morphisms, describe the corresponding deformation cohomology of morphisms, and show the properties of the cohomology. We prove its invariance under isomorphisms of morphisms. Additionally,…
A general procedure of affinization of linear algebra structures is illustrated by the case of Leibniz algebras. Specifically, the definition of an affine Leibniz bracket, that is, a bi-affine operation on an affine space that at each…
Morphisms between (formal) contexts are certain pairs of maps, one between objects and one between attributes of the contexts in question. We study several classes of such morphisms and the connections between them. Among other things, we…
We classify commutative algebraic monoid structures on normal affine surfaces over an algebraically closed field of characteristic zero. The answer is given in two languages: comultiplications and Cox coordinates. The result follows from a…
We construct the first examples of chamber-regular lattices on $\tilde C_2$-buildings. Assuming a conjecture of Kantor our list of examples becomes a classification for chamber-regular $\tilde C_2$-lattices on locally-finite $\tilde…
In this thesis we develop the foundations for a theory of analytic geometry over a valued field, uniformly encompassing the case when the base field is equipped with a non-archimedean valuation and the case when it has an archimedean one.…
We develop the structure theory of full isometry groups of locally compact non-positively curved metric spaces. Amongst the discussed themes are de Rham decompositions, normal subgroup structure and characterising properties of symmetric…
Starting with some motivating examples (classical atlases for a manifold, space of leaves of a foliation, group orbits), we propose to view a Lie groupoid as a generalized atlas for the "virtual structure" of its orbit space, the…