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Derived Hall algebras
"... The purpose of this work is to define a derived Hall algebra DH(T), associated to any dgcategory T (under some finiteness conditions). Our main theorem states that DH(T) is associative and unital. This provides an alternative to the nonexistence of Hall algebras for triangulated categories. Conten ..."
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The purpose of this work is to define a derived Hall algebra DH(T), associated to any dgcategory T (under some finiteness conditions). Our main theorem states that DH(T) is associative and unital. This provides an alternative to the nonexistence of Hall algebras for triangulated categories
A Categorification of Hall Algebras
, 2011
"... In recent years, there has been great interest in the study of categorification, specifically as it applies to the theory of quantum groups. In this thesis, we would like to provide a new approach to this problem by looking at Hall algebras. It is know, due to Ringel, that a Hall algebra is isomorph ..."
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In recent years, there has been great interest in the study of categorification, specifically as it applies to the theory of quantum groups. In this thesis, we would like to provide a new approach to this problem by looking at Hall algebras. It is know, due to Ringel, that a Hall algebra
Lectures on Hall algebras
, 2006
"... These notes represent the written, expanded and improved version of a series of lectures given at the winter school “Representation theory and related topics ” held at the ICTP in Trieste in January 2006. The topic for the lectures was “Hall algebras” and I have tried to give a survey of what I beli ..."
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These notes represent the written, expanded and improved version of a series of lectures given at the winter school “Representation theory and related topics ” held at the ICTP in Trieste in January 2006. The topic for the lectures was “Hall algebras” and I have tried to give a survey of what I
Derived Hall Algebras
"... ◮ E a finitary, exact category. ◮ H(E) an associative, unital algebra. ◮ Structure constants of H(E) encode the exact structure of E. H(E) is the RingelHall algebra of E. These were introduced by C.M. Ringel in 1990, generalising the construction of the classical Hall algebra. The Classical Hall Al ..."
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◮ E a finitary, exact category. ◮ H(E) an associative, unital algebra. ◮ Structure constants of H(E) encode the exact structure of E. H(E) is the RingelHall algebra of E. These were introduced by C.M. Ringel in 1990, generalising the construction of the classical Hall algebra. The Classical Hall
THE HALL ALGEBRA OF A SPHERICAL OBJECT
"... Abstract. We determine the Hall algebra, in the sense of Toën, of the algebraic triangulated category generated by a spherical object. 1. ..."
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Abstract. We determine the Hall algebra, in the sense of Toën, of the algebraic triangulated category generated by a spherical object. 1.
Hall Algebras as Hopf Objects
, 2010
"... One problematic feature of Hall algebras is the fact that the standard multiplication and comultiplication maps do not satisfy the bialgebra compatibility condition in the underlying symmetric monoidal category Vect. In the past this problem has been resolved by working with a weaker structure calle ..."
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One problematic feature of Hall algebras is the fact that the standard multiplication and comultiplication maps do not satisfy the bialgebra compatibility condition in the underlying symmetric monoidal category Vect. In the past this problem has been resolved by working with a weaker structure
HALL ALGEBRAS AND QUANTUM FROBENIUS.
, 2006
"... ABSTRACT. Lusztig has constructed a Frobenius morphism for quantum groups at an ℓth root of unity, which gives an integral lift of the Frobenius map on universal enveloping algebras in positive characteristic. Using the Hall algebra we give a simple construction of this map for the positive part of ..."
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ABSTRACT. Lusztig has constructed a Frobenius morphism for quantum groups at an ℓth root of unity, which gives an integral lift of the Frobenius map on universal enveloping algebras in positive characteristic. Using the Hall algebra we give a simple construction of this map for the positive part
SPHERICAL HALL ALGEBRAS OF CURVES AND
"... Abstract. We show that the characteristic function 1S of any HarderNarasimhan strata S CohX belongs to the spherical Hall algebra HsphX of a smooth projective curve X (dened over a nite eld Fq). We prove a similar result in the geometric setting: the intersection cohomology complex IC(S) of an ..."
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Abstract. We show that the characteristic function 1S of any HarderNarasimhan strata S CohX belongs to the spherical Hall algebra HsphX of a smooth projective curve X (dened over a nite eld Fq). We prove a similar result in the geometric setting: the intersection cohomology complex IC(S
Ringel–Hall algebras of cyclic quivers
 São Paulo J. Math. Sci
"... The Hall algebra, or algebra of partitions, was originally constructed in the context of abelian pgroups, and has a history going back to a talk by Steinitz [65]. This work was largely forgotten, leaving Hall to rediscover the algebra fifty years later [19]. (See also the articles [24, 38].) The Ha ..."
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The Hall algebra, or algebra of partitions, was originally constructed in the context of abelian pgroups, and has a history going back to a talk by Steinitz [65]. This work was largely forgotten, leaving Hall to rediscover the algebra fifty years later [19]. (See also the articles [24, 38
Results 1  10
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406