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Register a new userFinitary birepresentations of finitary bicategories
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In this paper, we discuss the generalization of finitary $2$-representation theory of finitary $2$-categories to finitary birepresentation theory of finitary bicategories. In previous papers on the subject, the classification of simple transitive $2$-representations of a given $2$-category was reduced to that for certain subquotients. These reduction results were all formulated as bijections between equivalence classes of $2$-representations. In this paper, we generalize them to biequivalences between certain $2$-categories of birepresentations. Furthermore, we prove an analog of the double centralizer theorem in finitary birepresentation theory.
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In this article, we study short exact sequences of finitary 2-representations of a weakly fiat 2-category. We provide a correspondence between such short exact sequences with fixed middle term and coidempotent subcoalgebras of a coalgebra 1-morphism defining this middle term. We additionally relate these to recollements of the underlying abelian 2-representations.
In this note we recall the importance of the notion of a finitary isomorphism in the classification problem of dynamical systems.
Let FL_s(K) be the finitary linear group of degree s over an associative ring K with unity. We prove that the torsion subgroups of FL_s(K) are locally finite for certain classes of rings K. A description of some f.g. solvable subgroups of FL_s(K) are given.
In this paper we investigate the concept of radical factorization with respect to finitary ideal systems of cancellative monoids. We present new characterizations for r-almost Dedekind r-SP-monoids and provide specific descriptions of t-almost Dedekind t-SP-monoids and w-SP-monoids. We show that a monoid is a w-SP-monoid if and only if the radical of every nontrivial principal ideal is t-invertible. We characterize when the monoid ring is a w-SP-domain and describe when the *-Nagata ring is an SP-domain for a star operation * of finite type.
We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically closed field of characteristic different from 2.
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