Related papers: Support varieties - an ideal approach
In \cite{BKN} the authors initiated a study of the representation theory of classical Lie superalgebras via a cohomological approach. Detecting subalgebras were constructed and a theory of support varieties was developed. The dimension of a…
The postulates of comprehension and extensionality in set theory are based on an inversion principle connecting set-theoretic abstraction and the property of having a member. An exactly analogous inversion principle connects functional…
We develop representation theory approach to the study of special functions associated with toric varieties. In particular we show that the corresponding special functions are given by matrix elements of certain non-reductive Lie algebras
Let $A$ be a homological category and $U\colon B\to A$ be a faithful conservative right adjoint. We introduce the notion of relative ideal with respect to $U$, and we show that, under suitable conditions, any object of $A$ can be seen as a…
An algorithm is presented that generates sets of size equal to the degree of a given variety defined by a homogeneous ideal. This algorithm suggests a versatile framework to study various problems in combinatorial algebraic geometry and…
We describe a new approach to the definition of the moduli functor of stable varieties. While there is wide agreement as to what classes of varieties should appear, the notion of a family of stable surfaces is quite subtle, as key numerical…
Support and rank varieties of modules over a group algebra of an elementary abelian p-group have been well studied. In particular, Avrunin and Scott showed that in this setting, the rank and support varieties are equivalent. Avramov and…
A global representation is a compatible collection of representations of the outer automorphism groups of the finite groups belonging to a family $\mathscr{U}$. These arise in classical representation theory, in the study of representation…
We introduce instancewise feature selection as a methodology for model interpretation. Our method is based on learning a function to extract a subset of features that are most informative for each given example. This feature selector is…
Ideals generated by adjacent 2-minors are studied. First, the problem when such an ideal is a prime ideal as well as the problem when such an ideal possesses a quadratic Gr\"obner basis is solved. Second, we describe explicitly a primary…
We initiate a systematic study of lattices of thick subcategories for arbitrary essentially small triangulated categories. To this end we give several examples illustrating the various properties these lattices may, or may not, have and…
Associated varieties are geometric objects appearing in infinite-dimensional representations of semisimple Lie algebras (groups). By applying Fourier transformations to the natural orthogonal oscillator representations of special linear Lie…
We develop a functorial framework for the ideal theory of commutative semirings using coherent frames and spectral spaces. Two central constructions-the radical ideal functor and the $k$-radical ideal functor-are shown to yield coherent…
The rules governing the essentially algebraic notion of a category with families have been observed (independently) by Steve Awodey and Marcelo Fiore to precisely match those of a representable natural transformation between presheaves.…
We define a diagrammatic monoidal category, together with a full and essentially surjective monoidal functor from this category to the category of modules over the exceptional Lie algebra of type $F_4$. In this way, we obtain a set of…
We classify the localizing tensor ideals of the integral stable module category for any finite group $G$. This results in a generic classification of $\mathbb{Z}[G]$-lattices of finite and infinite rank and globalizes the modular case…
We study ideals which are generated by monomials of degree $d$ in the polynomial ring in $n$ variables and which satisfy certain numerical side conditions regarding their exponents. Typical examples of such ideals are the ideals of Veronese…
A multi-type preferential attachment tree is introduced, and studied using general multi-type branching processes. For the $p$-type case we derive a framework for studying the tree where a type $i$ vertex generates new type $j$ vertices…
Interventional causal models describe several joint distributions over some variables used to describe a system, one for each intervention setting. They provide a formal recipe for how to move between the different joint distributions and…
From algebraic geometry perspective database relations are succinctly defined as Finite Varieties. After establishing basic framework, we give analytic proof of Heath theorem from Database Dependency theory. Next, we leverage…