scholarly journals ORBIFOLD CUP PRODUCTS AND RING STRUCTURES ON HOCHSCHILD COHOMOLOGIES

2011 ◽  
Vol 13 (01) ◽  
pp. 123-182 ◽  
Author(s):  
M. J. PFLAUM ◽  
H. B. POSTHUMA ◽  
X. TANG ◽  
H.-H. TSENG
Keyword(s):  
Cohomology Ring ◽  
Ring Structure ◽  
Hochschild Cohomology Ring ◽  
Convolution Algebras ◽  
First Case ◽  
De Rham ◽  
Ring Structures ◽  
Orbifold Cohomology ◽  
Cup Products ◽  
Equivariant Version

In this paper, we study the Hochschild cohomology ring of convolution algebras associated to orbifolds, as well as their deformation quantizations. In the first case, the ring structure is given in terms of a wedge product on twisted polyvectorfields on the inertia orbifold. After deformation quantization, the ring structure defines a product on the cohomology of the inertia orbifold. We study the relation between this product and an S1-equivariant version of the Chen–Ruan product. In particular, we give a de Rham model for this equivariant orbifold cohomology.

Hochschild Cohomology Ring of the Integral Group Ring of the Semidihedral 2-Group

2011 ◽  
Vol 18 (02) ◽  
pp. 241-258 ◽  
Author(s):  
Takao Hayami
Keyword(s):  
Group Ring ◽  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Ring Structure ◽  
Integral Group Ring ◽  
Integral Group ◽  
Hochschild Cohomology Ring

We determine the ring structure of the Hochschild cohomology HH*(ℤ G) of the integral group ring of the semidihedral 2-group G = SD2r of order 2r.

Cup-products for the polyhedral product functor

2012 ◽  
Vol 153 (3) ◽  
pp. 457-469 ◽  
Author(s):  
A. BAHRI ◽  
M. BENDERSKY ◽  
F. R. COHEN ◽  
S. GITLER
Keyword(s):  
Simplicial Complex ◽  
Cohomology Ring ◽  
Decomposition Theorem ◽  
Ring Structure ◽  
Polyhedral Product ◽  
Cup Product ◽  
Rational Cohomology ◽  
Geometric Decomposition ◽  
Abstract Simplicial Complex ◽  
Cup Products

AbstractDavis–Januszkiewicz introduced manifolds which are now known as moment-angle manifolds over a polytope [6]. Buchstaber–Panov introduced and extensively studied moment-angle complexes defined for any abstract simplicial complex K [4]. They completely described the rational cohomology ring structure in terms of the Tor-algebra of the Stanley-Reisner algebra [4].Subsequent developments were given in work of Denham–Suciu [7] and Franz [9] which were followed by [1, 2]. Namely, given a family of based CW-pairs X, A) = {(Xi, Ai)}mi=1 together with an abstract simplicial complex K with m vertices, there is a direct extension of the Buchstaber–Panov moment-angle complex. That extension denoted Z(K;(X,A)) is known as the polyhedral product functor, terminology due to Bill Browder, and agrees with the Buchstaber–Panov moment-angle complex in the special case (X,A) = (D2, S1) [1, 2]. A decomposition theorem was proven which splits the suspension of Z(K; (X, A)) into a bouquet of spaces determined by the full sub-complexes of K.This paper is a study of the cup-product structure for the cohomology ring of Z(K; (X, A)). The new result in the current paper is that the structure of the cohomology ring is given in terms of this geometric decomposition arising from the “stable” decomposition of Z(K; (X, A)) [1, 2]. The methods here give a determination of the cohomology ring structure for many new values of the polyhedral product functor as well as retrieve many known results.Explicit computations are made for families of suspension pairs and for the cases where Xi is the cone on Ai. These results complement and extend those of Davis–Januszkiewicz [6], Buchstaber–Panov [3, 4], Panov [13], Baskakov–Buchstaber–Panov, [3], Franz, [8, 9], as well as Hochster [12]. Furthermore, under the conditions stated below (essentially the strong form of the Künneth theorem), these theorems also apply to any cohomology theory.

scholarly journals Hochschild cohomology of some quantum complete intersections

2018 ◽  
Vol 17 (11) ◽  
pp. 1850215 ◽  
Author(s):  
Karin Erdmann ◽  
Magnus Hellstrøm-Finnsen
Keyword(s):  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Ring Structure ◽  
Complete Intersections ◽  
Root Of Unity ◽  
Nilpotent Elements ◽  
Hochschild Cohomology Ring ◽  
Quantum Complete Intersections ◽  
Primitive Formula

We compute the Hochschild cohomology ring of the algebras [Formula: see text] over a field [Formula: see text] where [Formula: see text] and where [Formula: see text] is a primitive [Formula: see text]th root of unity. We find the dimension of [Formula: see text] and show that it is independent of [Formula: see text]. We compute explicitly the ring structure of the even part of the Hochschild cohomology modulo homogeneous nilpotent elements.

Artefacts of SEM/TEM Observations Cases on Seal Ring Structure and Correctives Samples Preparations to Avoid Them

2019 ◽  
Author(s):  
Christophe Charles ◽  
Alain Margain
Keyword(s):  
Sample Preparation ◽  
Ring Structure ◽  
Seal Ring ◽  
Stress Tests ◽  
Preparation Methods ◽  
Process Modification ◽  
Sem And Tem ◽  
First Case ◽  
Key Factor ◽  
Ring Structures

Abstract FIB/SEM and TEM are standard characterization techniques for evaluation of process modification of microelectronics samples. In this paper, artefacts from these techniques are studied. The sample preparation methods are optimized to avoid damages. Seal-ring structures are chosen as an example in this study to show artefacts and difficulties in SEM and TEM observations. Two cases of artefacts are considered: one with TEM sample preparation followed by TEM imaging, and the other one with SEM observations after FIB cross-sectioning. In the first case, electronic chips that failed during stress tests are investigated, while in the second case a part has been dismissed during robustness qualification test. In the former, thickness of TEM lamellae has been evidenced as a key factor for delamination between layers under beam, whereas in the latter, it was observed that the electron beam lead to a shrink of oxide layers, which induced the break of underlying contacts.

On Hochschild cohomology ring and integral cohomology ring for the semidihedral group

2018 ◽  
Vol 28 (02) ◽  
pp. 257-290
Author(s):  
Takao Hayami
Keyword(s):  
Group Ring ◽  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Ring Structure ◽  
Integral Group Ring ◽  
Integral Group ◽  
Precise Description ◽  
Arbitrary Integer ◽  
Integral Cohomology ◽  
Hochschild Cohomology Ring

We will determine the ring structure of the Hochschild cohomology [Formula: see text] of the integral group ring of the semidihedral group [Formula: see text] of order [Formula: see text] for arbitrary integer [Formula: see text] by giving the precise description of the integral cohomology ring [Formula: see text] and by using a method similar to [T. Hayami, Hochschild cohomology ring of the integral group ring of the semidihedral [Formula: see text]-group, Algebra Colloq. 18 (2011) 241–258].

Parametric Instability of Dual-Ring Structure With Motionless and Moving Supports

2015 ◽  
Vol 11 (1) ◽  
Author(s):  
Zhifu Zhao ◽  
Shiyu Wang
Keyword(s):  
Parametric Instability ◽  
Ring Structure ◽  
Parametric Vibration ◽  
Rotating Speed ◽  
Ring Model ◽  
Ring Structures ◽  
Basic Parameters ◽  
Straight Lines ◽  
Transition Curves ◽  
Dual Ring

This work is to study parametric vibration of a dual-ring structure through analytical and numerical methods by focusing on the relationships between basic parameters and parametric instability. An elastic dual-ring model is developed by using Lagrange method, where the radial and tangential deflections are included, and motionless and moving supports are also incorporated. Analytical results imply that there are four kinds of parametric excitations, and the numerical results show that there exist stable and unstable areas separated by transition curves or straight lines, and even crossover points. The relationships are determined as simple expressions in basic parameters, including discrete stiffness number and wavenumber. Whether the parametric resonance can be excited or not depends on the values of support stiffness, rotating speed, and natural frequency. Vibrations at the crossover points are also addressed by using the multiscale method. Comparisons against the available results regarding ring structures with moving supports are also made. Extensions of this study, including the use of powerful Sinha method to deal with the parametric vibration, are suggested.

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