Displaying similar documents to “Quantum Cohomology and Crepant Resolutions: A Conjecture”

Overconvergent de Rham-Witt cohomology

Christopher Davis, Andreas Langer, Thomas Zink (2011)

Annales scientifiques de l'École Normale Supérieure

Similarity:

The goal of this work is to construct, for a smooth variety X over a perfect field k of finite characteristic p > 0 , an overconvergent de Rham-Witt complex W Ω X / k as a suitable subcomplex of the de Rham-Witt complex of Deligne-Illusie. This complex, which is functorial in X , is a complex of étale sheaves and a differential graded algebra over the ring W ( 𝒪 X ) of overconvergent Witt-vectors. If X is affine one proves that there is an isomorphism between Monsky-Washnitzer cohomology and (rational) overconvergent...

Exponentiations over the quantum algebra U q ( s l 2 ( ) )

Sonia L’Innocente, Françoise Point, Carlo Toffalori (2013)

Confluentes Mathematici

Similarity:

We define and compare, by model-theoretical methods, some exponentiations over the quantum algebra U q ( s l 2 ( ) ) . We discuss two cases, according to whether the parameter q is a root of unity. We show that the universal enveloping algebra of s l 2 ( ) embeds in a non-principal ultraproduct of U q ( s l 2 ( ) ) , where q varies over the primitive roots of unity.

A note on the cohomology ring of the oriented Grassmann manifolds G ˜ n , 4

Tomáš Rusin (2019)

Archivum Mathematicum

Similarity:

We use known results on the characteristic rank of the canonical 4 –plane bundle over the oriented Grassmann manifold G ˜ n , 4 to compute the generators of the 2 –cohomology groups H j ( G ˜ n , 4 ) for n = 8 , 9 , 10 , 11 . Drawing from the similarities of these examples with the general description of the cohomology rings of G ˜ n , 3 we conjecture some predictions.

Chen–Ruan Cohomology of 1 , n and ¯ 1 , n

Nicola Pagani (2013)

Annales de l’institut Fourier

Similarity:

In this work we compute the Chen–Ruan cohomology of the moduli spaces of smooth and stable n -pointed curves of genus 1 . In the first part of the paper we study and describe stack theoretically the twisted sectors of 1 , n and ¯ 1 , n . In the second part, we study the orbifold intersection theory of ¯ 1 , n . We suggest a definition for an orbifold tautological ring in genus 1 , which is a subring of both the Chen–Ruan cohomology and of the stringy Chow ring.

Effective Hamiltonians and Quantum States

Lawrence C. Evans (2000-2001)

Séminaire Équations aux dérivées partielles

Similarity:

We recount here some preliminary attempts to devise quantum analogues of certain aspects of Mather’s theory of minimizing measures [M1-2, M-F], augmented by the PDE theory from Fathi [F1,2] and from [E-G1]. This earlier work provides us with a Lipschitz continuous function u solving the eikonal equation aėȧnd a probability measure σ solving a related transport equation. We present some elementary formal identities relating certain quantum states ψ and u , σ . We show also how...

Remarks on Sekine quantum groups

Jialei Chen, Shilin Yang (2022)

Czechoslovak Mathematical Journal

Similarity:

We first describe the Sekine quantum groups 𝒜 k (the finite-dimensional Kac algebra of Kac-Paljutkin type) by generators and relations explicitly, which maybe convenient for further study. Then we classify all irreducible representations of 𝒜 k and describe their representation rings r ( 𝒜 k ) . Finally, we compute the the Frobenius-Perron dimension of the Casimir element and the Casimir number of r ( 𝒜 k ) .

Batalin-Vilkovisky algebra structures on Hochschild cohomology

Luc Menichi (2009)

Bulletin de la Société Mathématique de France

Similarity:

Let M be any compact simply-connected oriented d -dimensional smooth manifold and let 𝔽 be any field. We show that the Gerstenhaber algebra structure on the Hochschild cohomology on the singular cochains of M , H H * ( S * ( M ) , S * ( M ) ) , extends to a Batalin-Vilkovisky algebra. Such Batalin-Vilkovisky algebra was conjectured to exist and is expected to be isomorphic to the Batalin-Vilkovisky algebra on the free loop space homology on M , H * + d ( L M ) introduced by Chas and Sullivan. We also show that the negative cyclic...

Artinianness of formal local cohomology modules

Shahram Rezaei (2019)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let 𝔞 be an ideal of Noetherian local ring ( R , 𝔪 ) and M a finitely generated R -module of dimension d . In this paper we investigate the Artinianness of formal local cohomology modules under certain conditions on the local cohomology modules with respect to 𝔪 . Also we prove that for an arbitrary local ring ( R , 𝔪 ) (not necessarily complete), we have Att R ( 𝔉 𝔞 d ( M ) ) = Min V ( Ann R 𝔉 𝔞 d ( M ) ) .

Quantum expanders and geometry of operator spaces

Gilles Pisier (2014)

Journal of the European Mathematical Society

Similarity:

We show that there are well separated families of quantum expanders with asymptotically the maximal cardinality allowed by a known upper bound. This has applications to the “growth" of certain operator spaces: It implies asymptotically sharp estimates for the growth of the multiplicity of M N -spaces needed to represent (up to a constant C > 1 ) the M N -version of the n -dimensional operator Hilbert space O H n as a direct sum of copies of M N . We show that, when C is close to 1, this multiplicity grows...

On a number theoretic conjecture on positive integral points in a 5-dimensional tetrahedron and a sharp estimate of the Dickman–De Bruijn function

Ke-Pao Lin, Xue Luo, Stephen S.-T. Yau, Huaiqing Zuo (2014)

Journal of the European Mathematical Society

Similarity:

It is well known that getting the estimate of integral points in right-angled simplices is equivalent to getting the estimate of Dickman-De Bruijn function ψ ( x , y ) which is the number of positive integers x and free of prime factors > y . Motivating from the Yau Geometry Conjecture, the third author formulated the Number Theoretic Conjecture which gives a sharp polynomial upper estimate that counts the number of positive integral points in n-dimensional ( n 3 ) real right-angled simplices. In this...

Covariantization of quantized calculi over quantum groups

Seyed Ebrahim Akrami, Shervin Farzi (2020)

Mathematica Bohemica

Similarity:

We introduce a method for construction of a covariant differential calculus over a Hopf algebra A from a quantized calculus d a = [ D , a ] , a A , where D is a candidate for a Dirac operator for A . We recover the method of construction of a bicovariant differential calculus given by T. Brzeziński and S. Majid created from a central element of the dual Hopf algebra A . We apply this method to the Dirac operator for the quantum SL ( 2 ) given by S. Majid. We find that the differential calculus obtained by our...

On the generalized vanishing conjecture

Zhenzhen Feng, Xiaosong Sun (2019)

Czechoslovak Mathematical Journal

Similarity:

We show that the GVC (generalized vanishing conjecture) holds for the differential operator Λ = ( x - Φ ( y ) ) y and all polynomials P ( x , y ) , where Φ ( t ) is any polynomial over the base field. The GVC arose from the study of the Jacobian conjecture.

On a cubic Hecke algebra associated with the quantum group U q ( 2 )

Janusz Wysoczański (2010)

Banach Center Publications

Similarity:

We define an operator α on ℂ³ ⊗ ℂ³ associated with the quantum group U q ( 2 ) , which satisfies the Yang-Baxter equation and a cubic equation (α² - 1)(α + q²) = 0. This operator can be extended to a family of operators h j : = I j α I n - 2 - j on ( ³ ) n with 0 ≤ j ≤ n - 2. These operators generate the cubic Hecke algebra q , n ( 2 ) associated with the quantum group U q ( 2 ) . The purpose of this note is to present the construction.

Bounded cohomology and isometry groups of hyperbolic spaces

Ursula Hamenstädt (2008)

Journal of the European Mathematical Society

Similarity:

Let X be an arbitrary hyperbolic geodesic metric space and let Γ be a countable subgroup of the isometry group Iso ( X ) of X . We show that if Γ is non-elementary and weakly acylindrical (this is a weak properness condition) then the second bounded cohomology groups H b 2 ( Γ , ) , H b 2 ( Γ , p ( Γ ) ) ( 1 < p < ) are infinite dimensional. Our result holds for example for any subgroup of the mapping class group of a non-exceptional surface of finite type not containing a normal subgroup which virtually splits as a direct...

Cohomological dimension filtration and annihilators of top local cohomology modules

Ali Atazadeh, Monireh Sedghi, Reza Naghipour (2015)

Colloquium Mathematicae

Similarity:

Let denote an ideal in a Noetherian ring R, and M a finitely generated R-module. We introduce the concept of the cohomological dimension filtration = M i i = 0 c , where c = cd(,M) and M i denotes the largest submodule of M such that c d ( , M i ) i . Some properties of this filtration are investigated. In particular, if (R,) is local and c = dim M, we are able to determine the annihilator of the top local cohomology module H c ( M ) , namely A n n R ( H c ( M ) ) = A n n R ( M / M c - 1 ) . As a consequence, there exists an ideal of R such that A n n R ( H c ( M ) ) = A n n R ( M / H ( M ) ) . This generalizes the...

Results related to Huppert’s ρ - σ conjecture

Xia Xu, Yong Yang (2023)

Czechoslovak Mathematical Journal

Similarity:

We improve a few results related to Huppert’s ρ - σ conjecture. We also generalize a result about the covering number of character degrees to arbitrary finite groups.