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Search: All articles in the CJM digital archive with keyword duality

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1. CJM Online first

Asadollahi, Javad; Hafezi, Rasool; Vahed, Razieh
Bounded Derived Categories of Infinite Quivers: Grothendieck Duality, Reflection Functor
We study bounded derived categories of the category of representations of infinite quivers over a ring $R$. In case $R$ is a commutative noetherian ring with a dualising complex, we investigate an equivalence similar to Grothendieck duality for these categories, while a notion of dualising complex does not apply to them. The quivers we consider are left, resp. right, rooted quivers that are either noetherian or their opposite are noetherian. We also consider reflection functor and generalize a result of Happel to noetherian rings of finite global dimension, instead of fields.

Keywords:derived category, Grothendieck duality, representation of quivers, reflection functor
Categories:18E30, 16G20, 18E40, 16D90, 18A40

2. CJM Online first

Wu, Xinfeng
Weighted Carleson Measure Spaces Associated with Different Homogeneities
In this paper, we introduce weighted Carleson measure spaces associated with different homogeneities and prove that these spaces are the dual spaces of weighted Hardy spaces studied in a forthcoming paper. As an application, we establish the boundedness of composition of two Calderón-Zygmund operators with different homogeneities on the weighted Carleson measure spaces; this, in particular, provides the weighted endpoint estimates for the operators studied by Phong-Stein.

Keywords:composition of operators, weighted Carleson measure spaces, duality
Categories:42B20, 42B35

3. CJM 2009 (vol 61 pp. 1300)

Hubard, Isabel; Orbani\'c, Alen; Weiss, Asia Ivi\'c
Monodromy Groups and Self-Invariance
For every polytope $\mathcal{P}$ there is the universal regular polytope of the same rank as $\mathcal{P}$ corresponding to the Coxeter group $\mathcal{C} =[\infty, \dots, \infty]$. For a given automorphism $d$ of $\mathcal{C}$, using monodromy groups, we construct a combinatorial structure $\mathcal{P}^d$. When $\mathcal{P}^d$ is a polytope isomorphic to $\mathcal{P}$ we say that $\mathcal{P}$ is self-invariant with respect to $d$, or $d$-invariant. We develop algebraic tools for investigating these operations on polytopes, and in particular give a criterion on the existence of a $d$\nobreakdash-auto\-morphism of a given order. As an application, we analyze properties of self-dual edge-transitive polyhedra and polyhedra with two flag-orbits. We investigate properties of medials of such polyhedra. Furthermore, we give an example of a self-dual equivelar polyhedron which contains no polarity (duality of order 2). We also extend the concept of Petrie dual to higher dimensions, and we show how it can be dealt with using self-invariance.

Keywords:maps, abstract polytopes, self-duality, monodromy groups, medials of polyhedra
Categories:51M20, 05C25, 05C10, 05C30, 52B70

4. CJM 2005 (vol 57 pp. 204)

Xiong, Jie; Zhou, Xiaowen
On the Duality between Coalescing Brownian Motions
A duality formula is found for coalescing Brownian motions on the real line. It is shown that the joint distribution of a coalescing Brownian motion can be determined by another coalescing Brownian motion running backward. This duality is used to study a measure-valued process arising as the high density limit of the empirical measures of coalescing Brownian motions.

Keywords:coalescing Brownian motions, duality, martingale problem,, measure-valued processes
Categories:60J65, 60G57

5. CJM 1999 (vol 51 pp. 372)

Mytnik, Leonid
Uniqueness for a Competing Species Model
We show that a martingale problem associated with a competing species model has a unique solution. The proof of uniqueness of the solution for the martingale problem is based on duality technique. It requires the construction of dual probability measures.

Keywords:stochastic partial differential equation, Martingale problem, duality
Categories:60H15, 35R60

6. CJM 1999 (vol 51 pp. 3)

Allday, C.; Puppe, V.
On a Conjecture of Goresky, Kottwitz and MacPherson
We settle a conjecture of Goresky, Kottwitz and MacPherson related to Koszul duality, \ie, to the correspondence between differential graded modules over the exterior algebra and those over the symmetric algebra.

Keywords:Koszul duality, Hirsch-Brown model
Categories:13D25, 18E30, 18G35, 55U15

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