Related papers: Quantization in mixed polarization via transverse …

We describe the mod $p^r$ pro $K$-groups $\{K_n(A/I^s)/p^r\}_s$ of a regular local $\mathbb F_p$-algebra $A$ modulo powers of a suitable ideal $I$, in terms of logarithmic Hodge-Witt groups, by proving pro analogues of the theorems of…

In this paper we deduce the sketch of proof of the Duistermaat-Heckman formula and investigate how the known Duistermaat-Heckman result could be specialized to the symplectic structure on the orbit space. The theorems of localization in…

Fedosov used flat sections of the Weyl bundle on a symplectic manifold to construct a star product $\star$ which gives rise to a deformation quantization. By extending Fedosov's method, we give an explicit, analytic construction of a sheaf…

We study Lie algebroids from the point of view noncommutative geometry. More specifically, using ideas from deformation quantization, we use the PBW-theorem for Lie algebroids to construct a Fedosov-type resolution for the associated…

Using Kakichev's classical concept and extending Yakubovich-Britvina's approach (\textit{Results. Math.} 55(1-2):175-197, 2009) and (\textit{Integral Transforms Spec. Funct.} 21(4):259--276, 2010) for setting up Kontorovich-Lebedev…

Rota-Baxter associative algebras and Rota-Baxter Lie algebras are both important in mathematics and mathematical physics, with the former a basic structure in quantum field renormalization and the latter a operator form of the classical…

The purpose of this paper is to develop a new theory of gauges in mixed characteristic. Namely, let $k$ be a perfect field of characteristic $p>0$ and $W(k)$ the $p$-typical Witt vectors. Making use of Berthelot's arithmetic differential…

We show that the Poincar\'e lemma we proved elsewhere in the context of crystalline cohomology of higher level behaves well with regard to the Hodge filtration. This allows us to prove the Poincar\'e lemma for transversal crystals of level…

In their paper "Integrating curvature: From Umlaufsatz to J+ invariant" Lanzat and Polyak introduced a polynomial invariant of generic curves in the plane as a quantization of Hopf's Umlaufsatz, and showed that Arnold's J+ invariant could…

We develop a quantization scheme for the quantum theory of a real scalar field on a class of non-commutative spacetime models collectively known as T-Minkowski. Requiring the theory to be covariant under T-Poincar\'e transformations, we…

A duality is discussed for Lie group bundles vs. certain tensor categories with non-simple identity, in the setting of Nistor-Troitsky gauge-equivariant K-theory. As an application, we study C*-algebra bundles with fibre a fixed-point…

This work establishes a multivariable Wold-type decomposition for left-inverse commuting $n$-tuples of bounded operators, built on the hypothesis that each component admits a Wold-type decomposition. For pairs of operators, we obtain a…

The quantization properties of composite peripheric twists are studied. Peripheric chains of extended twists are constructed for U(sl(N)) in order to obtain composite twists with sufficiently large carrier subalgebras. It is proved that the…

The classical BKK theorem computes the intersection number of divisors on toric variety in terms of volumes of corresponding polytopes. It was observed by Pukhlikov and the first author that the BKK theorem leads to a presentation of the…

We consider new Abelian twists of Poincare algebra describing non-symmetric generalization of the ones given in [1], which lead to the class of Lie-deformed quantum Minkowski spaces. We apply corresponding twist quantization in two ways: as…

We review recent progress on operator mixing in the light of the theory of canonical forms for linear systems of differential equations and, in particular, of the Poincar\'e-Dulac theorem. We show that the matrix $A(g) =…

For a compact Lie group G, we use G-equivariant Poincar\'e duality for ordinary RO(G)-graded homology to define an equivariant intersection product, the dual of the equivariant cup product. Using this, we give a homological construction of…

Recently, Bocklandt proved a conjecture by Van den Bergh in its graded version, stating that a graded quiver algebra (with relations) which is Calabi-Yau of dimension 3 is defined from a homogeneous potential W. In this paper, we prove that…

K-theoretic Gromov-Witten invariants of a compact Kahler manifold $X$ are defined as super-dimensions of sheaf cohomology of interesting bundles over moduli spaces of n-pointed holomorphic curves in X. With this article, we begin a series…

The Chern classes of a K-theory class which is represented by a vector bundle with connection admit refinements to Cheeger-Simons classes in Deligne cohomology. In the present paper we consider similar refinements in the case where the…