3 We consider commuting squares of nite dimensional von Neumann algebras having the algebra of complex numbers in the lower left corner. Examples include the vertex models, the spin models (in the sense of subfactor theory) and the commuting squares associated to nite dimensional Kac algebras. To any such commuting square we associate a compact Kac algebra and we compute the corresponding subfa...

3 We consider commuting squares of nite dimensional von Neumann algebras having the algebra of complex numbers in the lower left corner. Examples include the vertex models, the spin models (in the sense of subfactor theory) and the commuting squares associated to nite dimensional Kac algebras. To any such commuting square we associate a compact Kac algebra and we compute the corresponding subfa...

BACKGROUND Vehicular traffic is a major source of outdoor air pollution in urban areas, and studies have shown that air pollution is worse during hours of commuting to and from work and school. However, it is unclear to what extent different commuting behaviors are a source of air pollution compared to non-commuters, and if air pollution exposure actually differs by the mode of commuting. This ...

Let D be a division ring, n 2 a natural number, and C ⊆ Mn(D). Two matrices A and B are called C−commuting if there is C ∈ C that AB−BA = C. In this paper the C−commuting graph of Mn(D) is defined and denoted by ΓC(Mn(D)). Conditions are given that guarantee that the C−commuting graph is connected.

Let D be a division ring, n 2 a natural number, and C ⊆ Mn(D). Two matrices A and B are called C−commuting if there is C ∈ C that AB−BA = C. In this paper the C−commuting graph of Mn(D) is defined and denoted by ΓC(Mn(D)). Conditions are given that guarantee that the C−commuting graph is connected.

We investigate the relation between the structure of a Moufang loop and its inner mapping group. Moufang loops of odd order with commuting inner mappings have nilpotency class at most two. 6-divisible Moufang loops with commuting inner mappings have nilpotency class at most two. There is a Moufang loop of order 2 with commuting inner mappings and of nilpotency class three.

In this paper we study various simplicial complexes associated to the commutative structure of a finite group G. We define NC(G) (resp. C(G)) as the complex associated to the poset of pairwise non-commuting (resp. commuting) sets of nontrivial elements in G. We observe that NC(G) has only one positive dimensional connected component, which we call BNC(G), and we prove that BNC(G) is simply conn...

The spatial distribution of households and firms, or urban spatial structure, is a core element of the study of urban economics and the crucial determinant of commuting patterns. This paper examines developments in the analysis of urban spatial structure and commuting that are related to the urban labour market that is the analysis of labour supply and labour demand in a spatial context. These ...

‎Let $mathcal{F}$ be an field of zero characteristic and $N_{infty‎}(‎mathcal{F})$ be the algebra of infinite strictly upper triangular‎ ‎matrices with entries in $mathcal{F}$‎, ‎and $f:N_{infty}(mathcal{F}‎)rightarrow N_{infty}(mathcal{F})$ be a non-additive Lie centralizer of $‎N_{infty }(mathcal{F})$; that is‎, ‎a map satisfying that $f([X,Y])=[f(X),Y]$‎ ‎for all $X,Yin N_{infty}(mathcal{F})...