Homology and cohomology of quantum complete intersections
نویسندگان
چکیده
منابع مشابه
(co)homology of Quantum Complete Intersections
We construct a minimal projective bimodule resolution for every finite dimensional quantum complete intersection of codimension two. Then we use this resolution to compute both the Hochschild cohomology and homology for such an algebra. In particular, we show that the cohomology vanishes in high degrees, while the homology is always nonzero.
متن کاملOn the semi-simplicity of the quantum cohomology algebras of complete intersections
In this short note, we study the semi-simplicity of the quantum cohomology algebras of smooth Fano complete intersections in projective space. Let V be a smooth Fano manifold with a symplectic form ω. The quantum cohomology on V is the cohomology H(V,Z{H2(V )}) with a ring structure defined by the GW-invariants. The Novikov ring Z{H2(V )} can be described as follows: choose a basis q1, · · · , ...
متن کاملThe Representation Dimension of Quantum Complete Intersections
We give a lower and an upper bound for the representation dimension of a quantum complete intersection.
متن کاملExt-SYMMETRY OVER QUANTUM COMPLETE INTERSECTIONS
We show that symmetry in the vanishing of cohomology holds for graded modules over quantum complete intersections. Moreover, symmetry holds for all modules if the algebra is symmetric.
متن کاملQuantum Cohomology of G/p and Homology of Affine Grassmannian
Let G be a simple and simply-connected complex algebraic group, P ⊂ G a parabolic subgroup. We prove an unpublished result of D. Peterson which states that the quantum cohomology QH∗(G/P ) of a flag variety is, up to localization, a quotient of the homology H∗(GrG) of the affine Grassmannian GrG of G. As a consequence, all three-point genus zero Gromov-Witten invariants of G/P are identified wi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2008
ISSN: 1937-0652
DOI: 10.2140/ant.2008.2.501