Related papers: A Basis Theorem for Rings with Commuting Operators…
We aim to give a self-contained and detailed yet simplified account of the foundations of the theory of double operator integrals, in order to provide an accessible entry point to the theory. We make two new contributions to these…
We compute the center of the ring of PD differential operators on a smooth variety over $\bZ/p^n\bZ$ confirming a conjecture of Kaledin. More generally, given an associative algebra $A_0$ over $\bF_p$ and its flat deformation $A_n$ over…
The purpose of this note is to verify that several basic rings appearing in transchromatic homotopy theory are Noetherian excellent normal domains and thus amenable to standard techniques from commutative algebra. In particular, we show…
In this paper we study one-point rank one commutative rings of difference operators. We find conditions on spectral data which specify such operators with periodic coefficients.
Arthur Cohn's irreducibility criterion for polynomials with integer coefficients and its generalization connect primes to irreducibles, and integral bases to the variable $x$. As we follow this link, we find that these polynomials are ready…
A major open question in the theory of Toeplitz operator on the Bergman space of the unit disk of the complex plane is the complete characterization of the set of all Toeplitz operators that commute with a given operator. In \cite{al}, the…
The theme of the paper is the question of existence and basic structure of transfer operators for endomorphisms of a unital C*-algebra. We establish a complete description of non-degenerate transfer operators, characterize complete transfer…
Kock [Bull. Austral. Math. Soc., 25 (1982), 357-386] has considered differential forms with values in a group in a context where neighborhood relations are available. By doing so, he has made it clear where the so-called Maurer-Cartan…
We show that by working over the absolute base $\mathbb S$ (the categorical version of the sphere spectrum) instead of $\mathbb S[\pm 1]$ improves our previous Riemann-Roch formula for $\overline{{\rm Spec\,}\mathbb Z}$. The formula equates…
A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…
This paper investigates the structure of generic motives and their implications for the motivic cohomology of fields. Originating in Voevodsky's theory of motives and related to Beilinson's vision of a motivic $t$-structure, generic motives…
We extend the Heine-Stieltjes Theorem to concern all (non-degenerate) differential operators preserving the property of having only real zeros. This solves a conjecture of B. Shapiro. The new methods developed are used to describe intricate…
We prove a variant of the so-called bilinear embedding theorem for operators in divergence form with complex coefficients and with nonnegative locally integrable potentials, subject to mixed boundary conditions, and acting on arbitrary open…
The main theorem here is the K-theoretic analogue of the cohomological `stable double component formula' for quiver functions in [Knutson, Miller, and Shimozono, math.AG/0308142]. This K-theoretic version is still in terms of lacing…
We study, by means of embeddings of Hilbert functions, a class of rings which we call Shakin rings, i.e. quotients K[X_1,...,X_n]/a of a polynomial ring over a field K by ideals a=L+P which are the sum of a piecewise lex-segment ideal L, as…
We show that Bloch's complex of relative zero-cycles can be used as a dualizing complex over perfect fields and number rings. This leads to duality theorems for torsion sheaves on arbitrary separated schemes of finite type over…
In this paper, we investigate the zero distributions of $q$-shift difference-differential polynomials of meromorphic functions with zero-order that extends and generalizes the classical Hayman results of the zeros of differential…
We give an algebraic proof for a theorem of Mislin in the case of cohomology of saturated fusion systems defined on p-groups when p is odd. Some applications of this theorem to block algebras of finite groups are also given.
In this paper we use the Lyndon-Shirshov basis to study the shuffle type polynomials. We give a free noncommutative binomial (or multinomial) theorem in terms of the Lyndon-Shirshov basis. Another noncommutative binomial theorem given by…
We introduce quasi-invariant polynomials for an arbitrary finite complex reflection group W. Unlike in the Coxeter case, the space Q_k of quasi-invariants of a given multiplicity is not, in general, an algebra but a module over the…