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J. J. Zhang

Publications and source records attributed to J. J. Zhang.

At least 37 records · Page 2Linked to original sources
arXiv2017

Noncommutative Auslander theorem

A version of Auslander theorem is proven for the following classes of noncommutative algebras: (a) noetherian PI local (or connected graded) algebras of finite injective dimension, (b) universal enveloping algebras of finite dimensional Lie algebras, and (c) noetherian graded down-up algebras.

math.RA↗
arXiv2016

Rigidity of down-up algebras with respect to finite group coactions

If a nontrivial finite group coacts on a graded noetherian down-up algebra $A$ inner faithfully and homogeneously, then the fixed subring is not isomorphic to $A$. Therefore graded noetherian down-up algebras are rigid with respect to finite group coactions, in the sense of Alev-Polo. An example is given to show that this rigidity under group coactions does not have all the same consequences as the rigidity under group actions.

math.RA↗
arXiv2016

Non-affine Hopf algebra domains of Gelfand-Kirillov dimension two

We classify all non-affine Hopf algebras $H$ over an algebraically closed field $k$ of characteristic zero that are integral domains of Gelfand-Kirillov dimension two and satisfy the condition $\text{Ext}^1_H(k, k) \neq 0$. The affine ones were classified by the authors in 2010.

math.RA↗
arXiv2015

Primitive Cohomology of Hopf algebras

Primitive cohomology of a Hopf algebra is defined by using a modification of the cobar construction of the underlying coalgebra. Among many of its applications, two classifications are presented. Firstly we classify all non locally PI, pointed Hopf algebra domains of Gelfand-Kirillov dimension two; and secondly we classify all pointed Hopf algebras of rank one. The first classification extends some results of Brown, Goodearl and others in an ongoing project to understand all Hopf algebras of low Gelfand-Kirillov dimension. The second generalizes results of Krop-Radford and Wang-You-Chen which classified Hopf algebras of rank one under extra hypothesis. Properties and algebraic structures of the primitive cohomology are discussed.

math.RA↗
arXiv2014

Connected Hopf algebras and iterated Ore extensions

We investigate when a skew polynomial extension T = R[x; σ, δ] of a Hopf algebra R admits a Hopf algebra structure, substantially generalising a theorem of Panov. When this construction is applied iteratively in characteristic 0 one obtains a large family of connected noetherian Hopf algebras of finite Gelfand-Kirillov dimension, including for example all enveloping algebras of finite dimensional solvable Lie algebras and all coordinate rings of unipotent groups. The properties of these Hopf algebras are investigated.

math.RA↗
arXiv2014

Is BZB J1450+5201 the most distant $γ$-ray BL Lacertae object?

BL Lacertae (BL Lac) objects at high redshifts ($z\geq 2$) are rarely detected. Through careful analysis of the SDSS spectrum, BZB J1450+5201 is confirmed to be a high-$z$ BL Lac object with $z\geq$ 2.471 by identifying the Ly$α$ 1216 and CIV 1548/1550 absorption lines. This indicates that BZB J1450+5201 is the most distant BL Lac object discovered to date. Careful analysis of the five-year \fermi data of 2FGL J1451.0+5159 shows that its $γ$-ray emission is robust with confidence level of 6.2$σ$ at 1-3 GeV and 6.7$σ$ at 3-10 GeV, and that the confusion of bright neighbor is negligible, which can not be fixed in the analysis of the two-year data. Meanwhile, 2FGL J1451.0+5159 is confirmed to be associated with BZB J1450+5201 using the five-year data. The analysis of multiwavelength data, from radio to $γ$-ray energies, indicates BZB J1450+5201 is an intermediate synchrotron peaked (ISP) source and consistent with distributions of other ISP sources at lower redshifts in the second LAT AGN catalog. The pure SSC model seems to be disfavoured, while scattering of weak external emission plus SSC process can provide a satisfactory description of the broadband emission.

astro-ph.HE↗
arXiv2013

SiGe quantum dots for fast hole spin Rabi oscillations

We report on hole g-factor measurements in three terminal SiGe self-assembled quantum dot devices with a top gate electrode positioned very close to the nanostructure. Measurements of both the perpendicular as well as the parallel g-factor reveal significant changes for a small modulation of the top gate voltage. From the observed modulations we estimate that, for realistic experimental conditions, hole spins can be electrically manipulated with Rabi frequencies in the order of 100MHz. This work emphasises the potential of hole-based nano-devices for efficient spin manipulation by means of the g-tensor modulation technique.

cond-mat.mes-hall↗
arXiv2013

Coassociative Lie algebras

A coassociative Lie algebra is a Lie algebra equipped with a coassociative coalgebra structure satisfying a compatibility condition. The enveloping algebra of a coassociative Lie algebra can be viewed as a coalgebraic deformation of the usual universal enveloping algebra of a Lie algebra. This new enveloping algebra provides interesting examples of noncommutative and noncocommutative Hopf algebras and leads to a classification of connected Hopf algebras of Gelfand-Kirillov dimension four in [WZZ].

math.RA↗
arXiv2011

Regular algebras of dimension 4 with 3 generators

We study Artin-Schelter regular algebras of global dimension 4 with three generators of degree one. We classify those which are domains and which have an additional Z x Z-grading, and prove that all of these examples are also strongly noetherian, Auslander regular, and Cohen-Macaulay.

math.RA↗
arXiv2010

Strain determination in the Si channel above a single SiGe island inside a field effect transistor using nanobeam x-ray diffraction

SiGe islands are used to induce tensile strain in the Si channel of Field Effect Transistors to achieve larger transconductance and higher current driveabilities. We report on x-ray diffraction experiments on a single fully-processed and functional device with a TiN+Al gate stack and source, gate, and drain contacts in place. The strain fields in the Si channel were explored using an x-ray beam focused to 400 nm diameter combined with finite element simulations. A maximum in-plane tensile strain of about 1% in the Si channel was found, which is by a factor of three to four higher than achievable for dislocation-free tensile strained Si in state-of-the-art devices.

cond-mat.mes-hall↗