Singular locally-scalar representations of quivers in Hilbert spaces and separating functions

2003/07/11 by I. K. Redchuk, Redchuk, I. K., A. V. Roiter +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT

paper · pdf · doi:10.48550/arxiv.math/0307166

14 pages. Report: International Conference on Algebras, Modules and Rings, Lisbon 2003 (by I. Redchuk)

arxiv created 2003/09/07 · arxiv updated 2009/12/01

Abstract

A numeric function ρ: ρ(k)=1+(k-1)/(k+1), k ∈ N was considered in [1]. In its terms criterions of finite representability and tameness of marked quivers, posets with equivalence and dyadic posets can be obtained; Dynkin schemes and extended schemes also can be characterized. In this paper authors consider the connection of function ρ with locally-scalar representations [2] of extended Dynkin graphs. Then a family of functions ρ_n is defined -- a generalization of function ρ, which plays an analogous part for more wide class of graphs. Also some properties of functions ρ and ρ_k are proved. References [1] L.A. Nazarova, A.V. Roiter. \it Norm of a relation, separating functions and representations of marked quivers. Ukr. Math. Jour., 54(2002), No.6, p.808-840. [2] S.A. Kruglyak, A.V. Roiter. \it Locally-scalar representations of graphs in the category of Hilbert spaces. Prepr. Ukr. Math. Jour. (2003).

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