相关论文: Finite presentation is a Morita invariant property
It was recently proven that the total multiplicity in the decomposition into irreducibles of the tensor product lambda x mu of two irreducible representations of a simple Lie algebra is invariant under conjugation of one of them; at a given…
In this paper, we complete the classification of representation-finite tensor product algebras in terms of quiver with relations.
We give a uniform construction that, on input of a recursive presentation $P$ of a group, outputs a recursive presentation of a torsion-free group, isomorphic to $P$ whenever $P$ is itself torsion-free. We use this to re-obtain a known…
We construct a finitely presented group with property (T) which can not act on on reasonable spaces. Such group is constructed using an generalization of Hall embedding theorem, where property (T) is added at the expense of weakening the…
We prove that every Ariki-Koike algebra is Morita equivalent to a direct sum of tensor products of smaller Ariki-Koike algebras which have q-connected parameter sets. A similar result is proved for the cyclotomic q-Schur algebras. Combining…
A modular fusion category C allows one to define projective representations of the mapping class groups of closed surfaces of any genus. We show that if all these representations are irreducible, then C has a unique Morita-class of simple…
We construct a 2-category version of tom Dieck's equivariant fundamental groupoid for representable orbifolds and show that the discrete fundamental groupoid is Morita invariant; hence an orbifold invariant for representable orbifolds.
We develop Morita theory for finitary additive 2-representations of finitary 2-categories. As an application we describe Morita equivalence classes for 2-categories of projective functors associated to finite dimensional algebras and for…
We use Bieri-Strebel invariants to determine when a normal fibre product in the product of two finitely presented groups is finitely presented. We give conditions that imply and in some cases characterize the existence of such finitely…
We show that atomic polyadic algebras of infinite dimensions are completely representable
We consider the functions in two variables on an arbitrary poset, for which the convolution operation is defined. We obtain the generalization of incidence algebra and describe its properties: invertibility, the Jackobson radical,…
Two finitely generated monoids are constructed, one finitely presented the other not, whose (directed, unlabelled) Cayley graphs are isomorphic.
The goal of this article is to describe several presentations of the infinity category of algebras over some monad on the infinity category of chain complexes.
We construct an example of an $A_{\infty}$ algebra structure defined over a finite dimensional graded vector space.
We prove that persistently finite algebras are not created by completions of algebras, in any ordered discriminator variety. A persistently finite algebra is one without infinite simple extensions. We prove that finite measurable relation…
We prove the following. Let $R$ be a Noetherian ring, $B$ a finitely generated $R$-algebra, and $A$ a pure $R$-subalgebra of $B$. Then $A$ is finitely generated over $R$.
The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to…
Let A be a connected graded noncommutative monomial algebra. We associate to A a finite graph \Gamma(A) called the CPS graph of A. Finiteness properties of the Yoneda algebra Ext_A(k,k) including Noetherianity, finite GK dimension, and…
We introduce Morita equivalence to the study of Kleene algebras and modules. Classical characterizations of Morita-equivalent semirings such as having equivalent categories of modules and one semiring being a full matrix algebra over the…
Our purpose is to prove the uniqueness of the representation for $G$-martingales with finite variation.