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Yang Han

Publications and source records attributed to Yang Han.

72 records · Page 4Linked to original sources
arXiv2016

A construction of dualizing categories by tensor products of categories

It is shown that the idempotent completion of the additive hull of the tensor product of the residue category of the category of paths of a locally finite quiver modulo an admissible ideal and a dualizing category is dualizing. Furthermore, the category of finitely presented functors over such tensor product category is dualizing and has almost split sequences. As applications, the categories of all kinds of complexes are proved to have almost split sequences.

math.RT↗
arXiv2016

On the mechanism of hydrophilicity of graphene

It is generally accepted that the hydrophilic property of graphene can be affected by the underlying substrate. However, the role of intrinsic vs. substrate contributions and the related mechanisms are vividly debated. Here we show that the intrinsic hydrophilicity of graphene can be intimately connected to the position of its Fermi level, which affects the interaction between graphene and water molecules. The underlying substrate, or dopants, can tune hydrophilicity by modulating the Fermi level of graphene. By shifting the Fermi level of graphene away from its Dirac point, via either chemical or electrical voltage doping, we show enhanced hydrophilicity with experiments and first principle simulations. Increased vapor condensation on graphene, induced by a simple shifting of its Fermi level, exemplifies applications in the area of interfacial transport phenomena.

cond-mat.mtrl-sci↗
arXiv2014

Reducing homological conjectures by n-recollements

n-recollements of triangulated categories and n-derived-simple algebras are introduced. The relations between the n-recollements of derived categories of algebras and the Cartan determinants, homological smoothness and Gorensteinness of algebras respectively are clarified. As applications, the Cartan determinant conjecture is reduced to 1-derived-simple algebras, and the Gorenstein symmetry conjecture is reduced to 2-derived-simple algebras.

math.RT↗
arXiv2014

A proof of extension conjecture

Extension conjecture states that if a simple module over an artin algebra has nonzero first self-extension group then it has nonzero i-th self-extension group for infinitely many positive integers i. It is shown by recollement of triangulated categories and differential graded homological algebra approach that extension conjecture is true for finite-dimensional elementary algebras over a field, particularly, for finite-dimensional algebras over an algebraically closed field. Moreover, bimodule approach is introduced to strong no loop conjecture, which provides two new proofs of Igusa-Liu-Paquette theorem.

math.RT↗
arXiv2013

Recollements and Hochschild theory

It is shown that a recollement of derived categories of algebras induces those of tensor product algebras and opposite algebras respectively, which is applied to clarify the relations between recollements of derived categories of algebras and smoothness and Hochschild cohomology of algebras.

math.RA↗
arXiv2013

Hattori-Stallings trace and character

It is shown that Hattori-Stallings trace induces a homomorphism of abelian groups, called Hattori-Stallings character, from the $K_1$-group of endomorphisms of the perfect derived category of an algebra to its zero-th Hochschild homology, which provides a new proof of Igusa-Liu-Paquette Theorem, i.e., the strong no loop conjecture for finite-dimensional elementary algebras, on the level of complexes. Moreover, the Hattori-Stallings traces of projective bimodules and one-sided projective bimodules are studied, which provides another proof of Igusa-Liu-Paquette Theorem on the level of modules.

math.KT↗
arXiv2012

Controllable-dipole quantum memory

We present a quantum memory protocol for photons that is based on the direct control of the transition dipole moment. We focus on the case where the light-matter interaction is enhanced by a cavity. We show that the optimal write process (maximizing the storage efficiency) is related to the optimal read process by a reversal of the {\it effective time} $τ=\int dt g^2(t)/κ$, where $g(t)$ is the time-dependent coupling and $κ$ is the cavity decay rate. We discuss the implementation of the protocol in a rare-earth ion doped crystal, where an optical transition can be turned on and off by switching a magnetic field.

quant-ph↗
arXiv2011

Transverse multi-mode effects on the performance of photon-photon gates

The multi-mode character of quantum fields imposes constraints on the implementation of high-fidelity quantum gates between individual photons. So far this has only been studied for the longitudinal degree of freedom. Here we show that effects due to the transverse degrees of freedom significantly affect quantum gate performance. We also discuss potential solutions, in particular separating the two photons in the transverse direction.

quant-ph↗
arXiv2010

Hochschild homology, global dimension, and truncated oriented cycles

It is shown that a bounded quiver algebra having a 2-truncated oriented cycle is of infinite Hochschild homology dimension and global dimension, which generalizes a result of Solotar and Vigué-Poirrier to nonlocal ungraded algebras having a 2-truncated oriented cycle of arbitrary length. Therefore, a bounded quiver algebra of finite global dimension has no 2-truncated oriented cycles. Note that the well-known "no loops conjecture", which has been proved to be true already, says that a bounded quiver algebra of finite global dimension has no loops, i.e., truncated oriented cycles of length 1. Moreover, it is shown that a monomial algebra having a truncated oriented cycle is of infinite Hochschild homology dimension and global dimension. Consequently, a monomial algebra of finite global dimension has no truncated oriented cycles.

math.RA↗
arXiv2010

Quantum repeaters based on Rydberg-blockade coupled atomic ensembles

We propose a scheme for realizing quantum repeaters with Rydberg-blockade coupled atomic ensembles, based on a recently proposed collective encoding strategy. Rydberg-blockade mediated two-qubit gates and efficient cooperative photon emission are employed to create ensemble-photon entanglement. Thanks to deterministic entanglement swapping operations via Rydberg-based two-qubit gates, and to the suppression of multi-excitation errors by the blockade effect, the entanglement distribution rate of the present scheme is higher by orders of magnitude than the rates achieved by other ensemble-based repeaters. We also show how to realize temporal multiplexing with this system, which offers an additional speedup in entanglement distribution.

quant-ph↗
arXiv2007

Superspecies and their representations

Superspecies are introduced to provide the nice constructions of all finite-dimensional superalgebras. All acyclic superspecies, or equivalently all finite-dimensional (gr-basic) gr-hereditary superalgebras, are classified according to their graded representation types. To this end, graded equivalence, graded representation type and graded species are introduced for finite group graded algebras.

math.RA↗
arXiv2006

Construction of Koszul algebras by finite Galois covering

It is shown that, the quasi-Koszulities of algebras and modules are Morita invariance. A finite-dimensional $K$-algebra $A$ with an action of $G$ is quasi-Koszul if and only if so is the skew group algebra $A \ast G$, where $G$ is a finite group satisfying $\char K \nmid |G|$. A finite-dimensional $G$-graded $K$-algebra $A$ is quasi-Koszul if and only if so is the smash product $A # G^*$, where $G$ is a finite group satisfying $\char K \nmid |G|$. These results are applied to prove that, if a finite-dimensional connected quiver algebra is Koszul then so are its Galois covering algebras with finite Galois group $G$ satisfying $\char K \nmid |G|$. So one can construct Koszul algebras by finite Galois covering. Moreover, a general construction of Koszul algebras by Galois covering with finite cyclic Galois group is provided. As examples, many Koszul algebras are constructed from exterior algebras and Koszul preprojective algebras by finite Galois covering with either cyclic or noncyclic Galois group.

math.RA↗
arXiv2005

Hochschild (co)homology of exterior algebras

The minimal projective bimodule resolutions of the exterior algebras are explicitly constructed. They are applied to calculate the Hochschild (co)homology of the exterior algebras. Thus the cyclic homology of the exterior algebras can be calculated in case the underlying field is of characteristic zero. Moreover, the Hochschild cohomology rings of the exterior algebras are determined by generators and relations.

math.RA↗
arXiv2005

Hochschild cohomology of truncated quiver algebras

For a truncated quiver algebra over a field of arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finite-dimensional if and only if its global dimension is finite if and only if its quiver has no oriented cycles.

math.RA↗
arXiv2005

Is tame open?

Is tame open? No answer so far. One may pose the Tame-Open Conjecture: Tame is open. But how to support it? No effective way to date. In this note, the rank of a wild algebra is introduced. The Wild-Rank Conjecture, which implies the Tame-Open Conjecture, is formulated. The Wild-Rank Conjecture is improved to the Basic-Wild-Rank Conjecture. A covering criterion on the rank of a basic wild algebra is given, which can be effectively applied to verify the Basic-Wild-Rank Conjecture for concrete algebras. It makes all conjectures much reliable.

math.RT↗
arXiv2005

Subrepresentations of Kronecker representations

Translated into the language of representations of quivers, a challenge in matrix pencil theory is to find sufficient and necessary conditions for a Kronecker representation to be a subfactor of another Kronecker representation in terms of their Kronecker invariants. The problem is reduced to a numerical criterion for a Kronecker representation to be a subrepresentation of another Kronecker representation in terms of their Kronecker invariants. The key to the problem is the calculation of ranks of matrices over polynomial rings. For this, a generalization and specialization approach is introduced. This approach is applied to provide a numerical criterion for a preprojective (resp. regular, preinjective) Kronecker representation to be a subrepresentation of another preprojective (resp. regular, preinjective) Kronecker representation in terms of their Kronecker invariants.

math.RT↗
arXiv2004

Hochschild (co)homology dimension

In 1989 Happel conjectured that for a finite-dimensional algebra $A$ over an algebraically closed field $k$, $\gl A< \infty$ if and only if $\hch A < \infty$. Recently Buchweitz-Green-Madsen-Solberg gave a counterexample to Happel's conjecture. They found a family of pathological algebra $A_q$ for which $\gl A_q = \infty$ but $\hch A_q=2$. These algebras are pathological in many aspects, however their Hochschild homology behaviors are not pathological any more, indeed one has $\hh A_q = \infty=\gl A_q$. This suggests to pose a seemingly more reasonable conjecture by replacing Hochschild cohomology dimension in Happel's conjecture with Hochschild homology dimension: $\gl A < \infty$ if and only if $\hh A < \infty$ if and only if $\hh A = 0$. The conjecture holds for commutative algebras and monomial algebras. In case $A$ is a truncated quiver algebras these conditions are equivalent to the quiver of $A$ has no oriented cycles. Moreover, an algorithm for computing the Hochschild homology of any monomial algebra is provided. Thus the cyclic homology of any monomial algebra can be read off in case the underlying field is characteristic 0.

math.RA↗