Related papers: Spherical subcategories in representation theory

We classify certain subcategories in quotients of exact categories. In particular, we classify the triangulated and thick subcategories of an algebraic triangulated category, i.e. the stable category of a Frobenius category.

We discuss a possible characterization, by means of forbidden configurations, of posets which are embeddable in a product of finitely many scattered chains.

For an arbitrary commutative ring k and t in k, we construct a 2-functor S_t which sends a tensor category to a new tensor category. By applying it to the representation category of a bialgebra we obtain a family of categories which…

In this paper we provide a preliminary investigation of subclasses of bounded posets with antitone involution which are "pastings" of their maximal Kleene sub-lattices. Specifically, we introduce super-paraorthomodular lattices, namely…

Originally a technical tool, the derived category of coherent sheaves over an algebraic variety has become over the last twenty years an important invariant in the birational study of algebraic varieties. Problems of birational invariance…

In this paper we are using the poset representation to describe the complex answers given by IR systems after a clustering and ranking processes. The answers considered may be given by cartographical representations or by thematic sub-lists…

In our previous papers we introduced categorical invariants, which are, roughly speaking, sets of triangulated subcategories in a given triangulated category and their quotients. Here is extended the list of examples, where these sets are…

Based on different views on the Jones polynomial we review representation theoretic categorified link and tangle invariants. We unify them in a common combinatorial framework and connect them via the theory of Soergel bimodules. The…

In algebraic quantum field theory the spacetime manifold is replaced by a suitable base for its topology ordered under inclusion. We explain how certain topological invariants of the manifold can be computed in terms of the base poset. We…

We introduce semisimple 2-categories, fusion 2-categories, and spherical fusion 2-categories. For each spherical fusion 2-category, we construct a state-sum invariant of oriented singular piecewise-linear 4-manifolds.

We define toric partial orders, corresponding to regions of graphic toric hyperplane arrangements, just as ordinary partial orders correspond to regions of graphic hyperplane arrangements. Combinatorially, toric posets correspond to finite…

These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…

There is a construction which lies at the heart of descent theory. The combinatorial aspects of this paper concern the description of the construction in all dimensions. The description is achieved precisely for strict n-categories and…

In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of…

Given a functor from any category into the category of topological spaces, one obtains a linear representation of the category by post-composing the given functor with a homology functor with field coefficients. This construction is…

The finitistic dimension of a triangulated category is introduced. For the category of perfect complexes over a ring it is shown that this dimension is finite if and only if the small finitistic dimension of the ring is finite.

In this paper, we present the implicit equations for one special class of real-valued spherical harmonics with octahedral symmetry. Based on this representation, we construct the rotationally invariant measure of deviation from the…

We give a full classification of representation types of the subcategories of representations of an $m \times n$ rectangular grid with monomorphisms (dually, epimorphisms) in one or both directions, which appear naturally in the context of…

We study triples of coisotropic or isotropic subspaces in symplectic vector spaces; in particular, we classify indecomposable structures of this kind. The classification depends on the ground field, which we only assume to be perfect and…

We put cluster tilting in ageneral framework by showing that any quotient of a triangulated category modulo a tilting subcategory (that is, a maximal one-orthogonal subcategory) carries an abelian structure. These abelian quotients turn out…