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Hall algebras associated to root categories

WebNov 15, 2024 · There are three typical constructions during this procedure. The first one is the realization of Kac-Moody algebras via Hall type Lie algebras of root categories given by Peng-Xiao [23]; the second one is the Drinfeld double of Hall algebras given by Xiao [28]; the third one is the derived Hall algebras introduced by Toën [27] and Xiao-Xu [29]. WebThe Hall polynomials are the structure constants of the Hall algebra. The Hall algebra plays an important role in the theory of Masaki Kashiwara and George Lusztig regarding …

Lie algebras arising from 1-cyclic perfect complexes

WebThe Hall type Lie algebras of root categories can also be used to realize Kac-Moody algebras, see Peng-Xiao [21] and Lin-Peng [14]. ... [18, 15], we will define a new kind of algebras associated to A in this section, called ∆-Hall algebras. 2.1. Ringel-HallalgebrasandGreen’sformula. First we will recall the definition of Ringel- WebSep 15, 2024 · Xiao J. Hall Algebra in A Root Category. Bielefeld: Bielefeld University, 1995. Google Scholar ... Xiao J, Xu F. Hall algebras associated to triangulated categories. Duke Math J, 2008, 143: 357–373. Article MathSciNet MATH Google Scholar Xiao J, Xu F. Remarks on Hall algebras of triangulated categories. Kyoto J Math, 2015, 55: 477–499 date format windows explorer https://prismmpi.com

[2210.12351] Hall algebras associated to root categories

WebApr 25, 2010 · Consider the canonical isomorphism between the positive part U + of the quantum group U q (g) and the Hall algebra H(Λ), where the semisimple Lie algebra g and the finite-dimensional hereditary algebra Λ share a Dynkin diagram. Chen and Xiao have given two algorithms to decompose the root vectors into linear combinations of … WebSep 15, 2024 · Xiao J. Hall Algebra in A Root Category. Bielefeld: Bielefeld University, 1995. Google Scholar ... Xiao J, Xu F. Hall algebras associated to triangulated … Webcomplexes uni bonn de pdf hall algebras associated to root categories researchgate prentice hall algebra 1 geometry ... scribd hall algebras and localization of categories desmos classroom activities prentice hall mathematics a g a table of contents savvas the hall algebra approach to quantum groups bivouac junction holiday camp

Quantum groups via Hall algebras of complexes - Annals of …

Category:On two Hall algebra approaches to odd periodic triangulated categories ...

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Hall algebras associated to root categories

Hall Algebras of Odd Periodic Triangulated Categories

WebNov 15, 2024 · The present paper mainly deals with Hall Lie algebras arising from the category of 1-cyclic perfect complexes over the path algebra of a Dynkin quiver Q. Let Γ be the underlying graph of Q. The set of iso-classes of objects in only depends on Γ, so will be denoted by (See Section 3.1 for details). We remind that the existence of Hall ... Web4 rows · Oct 22, 2024 · Hall algebras associated to root categories. Let be a finitary hereditary abelian category. We ...

Hall algebras associated to root categories

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WebWe prove that they are invariant under a big class of equivalences of stable categories. In Section 4, we relate our semi-derived Hall algebras to the derived Hall algebras of Toën and Xiao–Xu. In Section 5, we briefly discuss some examples. In Section 6, we outline some directions for future work. 2 Preliminaries 2.1 Hall algebras WebOct 22, 2024 · We define a Hall algebra for the root category of $\mathcal {A}$ by applying the derived Hall numbers of the bounded derived category... Giving Week! Show your …

WebOct 22, 2024 · Hall algebra and derived Hall algebra of a hereditary abelian category A in Section 2. In Section 3, we define a Hall algebra for the root category of A and prove …

WebSection 3 is devoted to investigate the root categories of representation-finite hereditary algebras. Such root categories characterize the algebras up to derived equivalence. In … WebAug 15, 2013 · Math. 140 (3) (2000) 563–603], the authors proved a theorem for constructing Hall type Lie algebras associated to 2-periodic triangulated categories. In particular, this theorem gives a global realization of symmetrizable Kac–Moody algebras. The purpose of this paper is to provide a refinement (meanwhile, a new proof) of the …

WebFurther, it was shown in [30, 33] that BGP-reflection functors induce isomorphisms of double Ringel–Hall algebras of quivers with distinct orientations, and their restrictions to the associated quantum enveloping algebras coincide with Lusztig’s symmetries. In some sense, BGP-reflection functors provide a categorification of Lusztig’s ...

WebNov 15, 2024 · HALL ALGEBRAS ASSOCIATED TO ROOT CATEGORIES. 2024, arXiv. Recommended articles (6) Research article. Hirzebruch-Riemann-Roch and Lefschetz type formulas for finite dimensional algebras. Journal of … date format with day nameWebDec 1, 2024 · In Sections 4 and 5 the actual calculations of Hall algebras are performed. Finally, in Section 6 we explain how these calculations apply to a description of the Hall algebras associated to the derived categories of the one-cycle gentle algebras of infinite global dimension. Throughout the paper F is a fixed finite field of cardinality q. date format win 11WebDec 3, 2011 · Abstract. We define the Hall algebra associated to any triangulated category under some finiteness conditions with odd periodic translation functor T. This generalizes the results in Toën (Duke Math J 135 (3):587–615, 2006) and Xiao and Xu (Duke Math J 143 (2):357–373, 2008 ). Download to read the full article text. date format while mail mergeWebOct 22, 2024 · Hall algebras associated to root categories. Let be a finitary hereditary abelian category. We define a Hall algebra for the root category of by applying the derived Hall numbers of the bounded derived category , which is proved to be isomorphic to the Drinfeld double Hall algebra of . In the appendix, we also define the 1-periodic derived … bivouac militaryWebfollowing the idea in [23], there are (generic) Hall Lie algebras associated with the root categories of Db(O(~x)⊥) and Db(⊥O(~x)) both of which are isomorphic to the Hall Lie algebra of Q. In particular, their composition Lie subalgebras are all isomorphic to the Kac–Moody algebra gQ. We then show that the mutation functors mentioned bivouac newmarketWebbra associated to Peng and Xiao’s root category, which is, roughly speaking, the derived category of the category of this abelian category of representa-tions, modulo a double shift relation [15]. In [22], To¨en constructs “derived Hall algebras” associated to triangu-lated categories arising as homotopy categories of model categories whose bivouac lot of starsWebOct 17, 2013 · The (classical) Hall algebra over a commutative ring R with a parameter q ∈ R is defined to be the free R -module with basis ( I λ), where λ runs over all integer … bivouac new york