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In this paper we start a classification of certain global integrals. First, we use the language of unipotent orbits to write down a family of global integrals. We then classify all those integrals which satisfy the dimension equation we…

Representation Theory · Mathematics 2015-04-09 David Ginzburg

A finite EI category is a small category with finitely many morphisms such that every endomorphism is an isomorphism. They include finite groups, finite posets and free categories of finite quivers as special cases. In this paper we…

Representation Theory · Mathematics 2013-11-07 Liping Li

The global dimension of a triangulated category is defined to be the infimum value of the global dimensions of stability conditions on the triangulated category. In this paper, we study the global dimension of the derived category of an…

Algebraic Geometry · Mathematics 2025-02-03 Takumi Otani

A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading (including the trivial grading). We show that a…

Rings and Algebras · Mathematics 2019-12-30 Yuri Bahturin , Alberto Elduque , Mikhail Kochetov

Let $\md^b(A)$ be the derived category of a finite dimensional basic algebra $A$ with finite global dimension. We construct the Lie algebra arising from the 2-periodic version $\mk_2(\mp(A))$ of $\mk^b(\mp(A))$ in term of constructible…

Quantum Algebra · Mathematics 2010-01-27 Jie Xiao , Fan Xu , Guanglian Zhang

In this article we study homotopes of finite-dimensional algebras (not necessarily, associative). In the case of associative algebras we study homotopes by methods of Category theory and give description of so-called well-tempered elements…

Rings and Algebras · Mathematics 2020-05-05 Ilya Zhdanovskiy

We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of…

Representation Theory · Mathematics 2012-01-24 Yuriy A. Drozd , Eugene A. Kubichka

A finite directed category is a $k$-linear category with finitely many objects and an underlying poset structure, where $k$ is an algebraically closed field. This concept unifies structures such as $k$-linerizations of posets and finite EI…

Representation Theory · Mathematics 2013-11-07 Liping Li

Let C be the category of finite-dimensional representations of a quantum affine algebra of simply-laced type. We introduce certain monoidal subcategories C_l (l integer) of C and we study their Grothendieck rings using cluster algebras.

Quantum Algebra · Mathematics 2019-12-19 David Hernandez , Bernard Leclerc

We define a dimension for a triangulated category. We prove a representabilityTheorem for a certain class of functors on finite dimensional triangulatedcategories. We study the dimension of the boundedderived category of an algebra or a…

Category Theory · Mathematics 2007-05-23 Raphael Rouquier

We develop new techniques to classify basic algebras of blocks of finite groups over algebraically closed fields of prime characteristic. We apply these techniques to simplify and extend previous classifications by Linckelmann, Murphy and…

Representation Theory · Mathematics 2023-01-26 Dave Benson , Benjamin Sambale

We compute the Krull-Gabriel dimension of the category of perfect complexes for finite dimensional algebras which are derived discrete.

Representation Theory · Mathematics 2014-02-10 Grzegorz Bobinski , Henning Krause

In this paper we give an explicit algorithm to construct the ordinary quiver of a finite EI category for which the endomorphism groups of all objects have orders invertible in the field k. We classify all finite EI categories with…

Representation Theory · Mathematics 2013-11-07 Liping Li

The paper is devoted to classification problem of finite dimensional complex none Lie filiform Leibniz algebras. The motivation to write this paper is an unpublished yet result of J.R.Gomez, B.A.Omirov on necessary and sufficient conditions…

Rings and Algebras · Mathematics 2007-05-23 U. D. Bekbaev , I. S. Rakhimov

For finitary regular monads T on locally finitely presentable categories we characterize the finitely presentable objects in the category of T-algebras in the style known from general algebra: they are precisely the algebras presentable by…

Category Theory · Mathematics 2019-09-06 Jiří Adámek , Stefan Milius , Lurdes Sousa , Thorsten Wißmann

We show that the category of truncated spaces with finite homotopy invariants ($\pi$\=/finite spaces) has many of the features expected of an elementary \oo topos. It should be thought of as the natural higher analogue of the elementary…

Category Theory · Mathematics 2025-03-05 Mathieu Anel

We classify the thick subcategories of an algebraic triangulated standard category with finitely many indecomposable objects.

Category Theory · Mathematics 2010-10-04 Claudia Köhler

We study generic objects in triangulated categories and characterize the finite dimensional algebras $A$ such that the derived categories $D(\Mod A)$ are generically trivial. This is an analogue of a result of Crawley-Boevey for module…

Representation Theory · Mathematics 2014-12-03 Han Zhe

We develop a unified categorical framework for gauging both continuous and finite symmetries in arbitrary spacetime dimensions. Our construction applies to geometric categories i.e. categories internal to stacks. This generalizes the…

Mathematical Physics · Physics 2026-01-26 Devon Stockall , Matthew Yu

We consider and characterize classes of finite and countably categorical structures and their theories preserved under $E$-operators and $P$-operators. We describe $e$-spectra and families of finite cardinalities for structures belonging to…

Logic · Mathematics 2017-01-04 Sergey V. Sudoplatov