Quantum Grothendieck rings and derived Hall algebras
نویسندگان
چکیده
منابع مشابه
Algebras in Quantum Hall Theory
We show that U(∞) symmetry transformations of the noncommutative field theory in the Moyal space are generated by a combination of twoW1+∞ algebras in the Landau problem. Geometrical meaning of this infinite symmetry is illustrated by examining the transformations of an invariant subgroup on the noncommutative solitons, which generate deformations and boosts of solitons. In particular, we find ...
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The resulting algebra is known as the Hall algebra HA of A. Hall algebras first appeared in the work of Steinitz [S] and Hall [H] in the case where A is the category of Abelian p-groups. They reemerged in the work of Ringel [R1]-[R3], who showed in [R1] that when A is the category of quiver representations of an A-D-E quiver ~ Q over a finite field Fq, the Hall algebra of A provides a realizati...
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The aim of the present paper is to introduce a generalized quantum cluster character, which assigns to each object V of a finitary Abelian category C over a finite field Fq and any sequence i of simple objects in C the element XV,i of the corresponding algebra PC,i of q-polynomials. We prove that if C was hereditary, then the assignments V 7→ XV,i define algebra homomorphisms from the (dual) Ha...
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In [1],the authors defined algebra homomorphisms from the dual RingelHall algebra of certain hereditary abelian categoryA to an appropriate q-polynomial algebra. In the case that A is the representation category of an acyclic quiver, we give an alternative proof by using the cluster multiplication formulas in [9]. Moreover, if the underlying graph of Q is bipartite and the matrix B associated t...
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2013
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle-2013-0020