The category of coherent sheaves over a weighted projective line and loop algebras
نویسندگان
چکیده
منابع مشابه
Koszul Algebras and Sheaves over Projective Space
We are going to show that the sheafication of graded Koszul modules KΓ over Γn = K [x0, x1...xn] form an important subcategory ∧ KΓ of the coherents sheaves on projective space, Coh(P n). One reason is that any coherent sheave over P n belongs to ∧ KΓup to shift. More importantly, the category KΓ allows a concept of almost split sequence obtained by exploiting Koszul duality between graded Kosz...
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We notice that, for branes wrapped on complex analytic subvarieties, the algebraic-geometric version of K-theory makes the identification between brane-antibrane pairs and lower-dimensional branes automatic. This is because coherent sheaves on the ambient variety represent gauge bundles on subvarieties, and they can be put in exact sequences (pro-jective resolutions) with sheaves corresponding ...
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A well-known conjecture says that every one-relator group is coherent. We state and partly prove a similar statement for graded associative algebras. In particular, we show that every Gorenstein algebra A of global dimension 2 is graded coherent. This allows us to define a noncommutative analogue of the projective line P as a noncommutative scheme based on the coherent noncommutative spectrum q...
متن کاملNoncommutative Projective Curves and Quantum Loop Algebras
We show that the Hall algebra of the category of coherent sheaves on a weighted projective line over a finite field provides a realization of the (quantized) enveloping algebra of a certain nilpotent subalgebra of the affinization of the corresponding Kac-Moody algebra. In particular, this yields a geometric realization of the quantized enveloping algebra of elliptic (or 2-toroidal) algebras of...
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ژورنال
عنوان ژورنال: SCIENTIA SINICA Mathematica
سال: 2018
ISSN: 1674-7216
DOI: 10.1360/n012018-00011