Related papers: About Dixmier's conjecture

We use the holomorphic anomaly equation to solve the gravitational corrections to Seiberg-Witten theory and a two-cut matrix model, which is related by the Dijkgraaf-Vafa conjecture to the topological B-model on a local Calabi-Yau manifold.…

Let $G$ be a connected Lie group, with Lie algebra $g$. In 1977, Duflo constructed a homomorphism of $g$-modules $Duf: S(g) -> U(g)$, which restricts to an algebra isomorphism on invariants. Kashiwara and Vergne (1978) proposed a conjecture…

We show that the automorphism group of every zero entropy infinite shift admits a "drift" homomorphism to $(\mathbb{R},+)$ that maps the shift map to 1. This homomorphism arises as the expectation, under an invariant measure, of a cocycle…

We call an algebra $A$ commutator-simple if $[A,A]$ does not contain nonzero ideals of $A$. After providing several examples, we show that in these algebras derivations are determined by a condition that is applicable to the study of local…

The asymptotic behaviour of solutions to the quantum differential equation of a Fano manifold F defines a characteristic class A_F of F, called the principal asymptotic class. Gamma conjecture of Vasily Golyshev and the present authors…

The group of automorphisms is found for the Lie algebra of polynomial vector fields with constant divergence.

We compute the alpha invariant of any smooth complex projective spin complete intersection of complex dimension $1 \; ({\rm mod} \; 4)$. We prove that the alpha invariant depends only on the total degree and Pontryagin classes. Our findings…

The monodromy conjecture is a mysterious open problem in singularity theory. Its original version relates arithmetic and topological/geometric properties of a multivariate polynomial $f$ over the integers, more precisely, poles of the…

Let Dtt denote the set of truth-table degrees. A bijection p from Dtt to Dtt is an automorphism if for all truth-table degrees x and y we have x <=tt y if and only if p(x) <=tt p(y). We say an automorphism p is fixed on some cone if there…

We show that assuming the standard conjectures, for any smooth projective variety $X$ of dimension $n$ over an algebraically closed field, there is a constant $C>0$ such that for any positive rational number $r$ and for any polarized…

Let $q$ be an algebraic Lie algebra and $q<m>$ a (generalised) Takiff algebra. Any finite order automorphism $\theta$ of $q$ induces an automorphisms of $q<m>$ of the same order, denoted $\Theta$. We study invariant-theoretic properties of…

In this note, we are interested in the Jacobian Conjecture. Following the results of L.M.~Dru$\dot{\rm z}$kowski, we consider some vector fields depending on a certain \'etale polynomial map. From results of semialgebraic geometry with the…

We consider the following conjecture (from Huang, et al): Let $\Delta^+$ denote the upper half disc in $\mathbb{C}$ and let $\gamma = ( - 1, 1)$ (viewed as an interval in the real axis in $\mathbb{C}$). Assume that $F$ is a holomorphic…

Given a variety of universal algebras. A method is suggested for describing automorphisms of a category of free algebras of this variety. Applying this general method all automorphisms of such categories are found in two cases: 1) for the…

In this paper we find all permutations of the level k weights of the affine algebra A_r^{(1)} which commute with both its S and T modular matrices. We find that all of these are simple current automorphisms and their conjugations.…

Let $A_2$ be a free associative or polynomial algebra of rank two over a field $K$ of characteristic zero. Based on the degree estimate of Makar-Limanov and J.-T.Yu, we prove: 1) An element $p \in A_2$ is a test element if $p$ does not…

For any algebraically closed field $K$ and any endomorphism $f$ of $\mathbb{P}^1(K)$ of degree at least 2, the automorphisms of $f$ are the M\"obius transformations that commute with $f$, and these form a finite subgroup of…

Thanks to recent results on ring homomorphisms of Azumaya algebras and to the following ones about endomorphisms of canonical Poisson algebras and Dirac quantum algebras, and about the reformulation in positive characteristic of these…

Given a countable abelian group $A$, we construct a row finite directed graph $\Gamma(A)$ such that the $K_{0}$-group of the graph $\textrm{C}^{\ast}$-algebra $\textrm{C}^{\ast}(\Gamma(A))$ is canonically isomorphic to $A$. Moreover, each…

Let $f:X\to X$ be a non-isomorphic (i.e., $\text{deg } f>1$) surjective endomorphism of a smooth projective threefold $X$. We prove that any birational minimal model program becomes $f$-equivariant after iteration, provided that $f$ is…