相关论文: Dixmier's Problem 5 for the Weyl Algebra
Holonomy algebras of Weyl connections in Lorentzian signature are classified. In particular, examples of Weyl connections with all possible holonomy algebras are constructed.
We derive sufficient conditions for the existence of the Weber formal solution of the corresponding integral equation, related to the familiar Weber-Orr integral transforms. This gives a solution to the old Weber-Titchmarsh problem (posed…
We establish the converse of Weyl's eigenvalue inequality for additive Hermitian perturbations of a Hermitian matrix.
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.
Zagier provided eleven conjectural rank two examples for Nahm's problem. All of them have been proved in the literature except for the fifth example, and there is no $q$-series proof for the tenth example. We prove that the fifth and the…
In this short note we confirm an analog of a conjecture of James Wiegold for finite dimensional nilpotent Lie algebras.
We give a proof for the decidability of the HD0L ultimate periodicity problem.
Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.
We define and study the counterpart of the Wiener algebra in the quaternionic setting, both for the discrete and continuous case. We prove a Wiener-L\'evy type theorem and a factorization theorem. We give applications to Toeplitz and…
We analyze a variety of Weyl invariant dynamical problems in three dimensions.
We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.
We formulate and prove the Siegel-Weil formula for loop groups.
Several open problems in algebraic logic are solved.
We present an elementary proof of the irrationality of $\zeta(5)$ based upon the Dirichlet's approximation theorem and the Prime Number Theorem.
One more solution of 2D Ising model is found
In this paper the Navier problem and the Dirichlet problem for Willmore curves in $\mathbb{R}^2$ is solved.
In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].
Let $A_1:=K\langle x, \frac{d}{dx} \rangle$ be the Weyl algebra and $\mI_1:= K\langle x, \frac{d}{dx}, \int \rangle$ be the algebra of polynomial integro-differential operators over a field $K$ of characteristic zero. The Conjecture/Problem…
We find a counterexample to Feit's Problem VIII on the bound of decomposition numbers. This also answers a question raised by T. Holm and W. Willems.
The inversion formula is given for automorphisms of the Weyl algebras with polynomial coefficients over a field of characteristic zero. The theorem of Gabber on the degree of polynomial automorphism is extended. It is proved that any…