Some Algebras Associated to Automorphisms of Elliptic Curves

By M. Artin, J. Tate, Michel van den Bergh. 2007

376 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/794dac3a165b2b4d8614b1fa7bab40af1598085b

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Citations in the corpus

Generalizations of graded Clifford algebras and of complete intersections (2010, methodology): “In the spirit of [2], we write Γ2 = V(U) ⊂ P(V ) × P(V ), and we use Γ1 ⊂ P(V ) to denote the image of the projection of Γ2 onto the first copy of P(V ).”
Calabi-Yau algebras (2006, neutral): “lyanin algebras). Keep F= Chx,y,zi. Given a triple a,b,c∈C,we put Φ = axyz+byxz+c(x3 +y3 +z3). 3 The corresponding algebra A(F,Φ) is called quadratic Sklyanin algebra. The original deﬁnition in [AS], [ATV], [VdB2] was not given in this form but is equivalent to ours, as can be readily seen from e.g.”
Higher symplectic reflection algebras and non-homogeneous N-Koszul property (2005, methodology): “The fact that p : A → gr(U) is an isomorphism allows us to deduce properties of U from those of A. For example, using [ 2 , 3], U(α, β, γ) is a noetherian domain of Gelfand-Kirillov dimension 3 (see also [5]).”
Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves (2005, background): “is isomorphic to the functor›O(K)[ 2 ]; whereO(K) is the canonical line bundle.”
Quasi-Deformations of 𝔰𝔩2(𝔽) Using Twisted Derivations (2005, background): “The Artin–Schelter regular algebras with homogeneous defining relations (and more generally Auslanderregular algebras) turned out to be a most natural choice for a non-commutative projective geometry and this stimulated a directed effort in understanding the various homological and geometric propert”
SMOOTH AND PROPER NONCOMMUTATIVE SCHEMES AND GLUING OF DG CATEGORIES (2014, background): “case of noncommutative projective planes, in sense of noncommutative deformations of the usual projective plane, which have been introduced and described by M. Artin, J. Tate, and M. Van den Bergh in [ATV]. The author is very grateful to Valery Alexeev, Alexei Bondal, Sergei Gorchinskiy, Anton Fonar”
Quadratic algebras, Yang-Baxter equation, and Artin-Schelter regularity (2010, background): “, their classication, and nding new classes of such rings is one of the basic problems for noncommutative geometry. Numerous works on this topic appeared during the last two decades, see for example [4, 5], [7], [28], [43], [30], et all. A class of PBW AS regular algebras of global dimension nwas in”
On triangulated orbit categories (2005, background): “W orse,in ‘m ost’cases,it is im possible to endow T =F with a triangulated structure such that the projection functor becom es a triangle functor.”