N. D. Popova

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Articles: 2

On *-representations of a class of algebras with polynomial growth related to Coxeter graphs

N. D. Popova, A. V. Strelets

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 17 (2011), no. 3, 252-273

For a Hilbert space $H$, we study configurations of its subspaces related to Coxeter graphs $\mathbb{G}_{s_1,s_2}$, $s_1,s_2\in\{4,5\}$, which are arbitrary trees such that one edge has type~$s_1$, another one has type~$s_2$ and the rest are of type~$3$. We prove that such irreducible configurations exist only in a finite dimensional $H$, where the dimension of $H$ does not exceed the number of vertices of the graph by more than twice. We give a description of all irreducible nonequivalent configurations; they are indexed with a continuous parameter. As an example, we study irreducible configurations related to a graph that consists of three vertices and two edges of type $s_1$ and $s_2$.

On finite dimensional representations of one algebra of Temperly-Lieb type

N. D. Popova

Methods Funct. Anal. Topology 7 (2001), no. 3, 80-92

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