Related papers: Witt vectors, commutative and non-commutative

In this paper, we show how to split the writhe of reduced projections of oriented alternating links into two parts, called nullification writhe, or wx, and remaining writhe, or wy, such that the sum of these quantities equals the writhe w,…

There have been comments on the starting paper, hep-th/0106074, which point out unclear motivation and definitions on noncommutative momentum introduced. This paper is withdrawn by the author for more clear presentation.

We establish dimension formulas for the Witt vector affine Springer fibers associated to a reductive group over a mixed characteristic local field, under the assumption that the group is essentially tamely ramified and the residue…

We compute the algebraic K-theory of the non-commutative ring k<x_1,...,x_n>/(m^a) when k is a perfect field of positive characteristic and m=(x_1,...,x_n). We express the answer in terms of the truncation poset Witt vectors developed in…

I compiled a list of articles on arXiv that deal with possible fundamental quantum nonlinearities or examine the origins of its linearity. The list extends til August 2004.

We obtain the leading derivative corrections to an expression for the Seiberg-Witten map given by Banerjee and Yang and show how they affect the noncommutative deformation of the Maxwell action, as well as the matter coupling in…

This paper is a revised version of a previously posted paper in arxiv. The authors posted it as a new submission by mistake. The latest version of the paper can be found at arXiv:math-ph/0512003v2

The complete characterizations of the spectra and their various parts of hyponormal unilateral and bilateral weighted shifts are presented respectively in this paper. The results obtained here generalize the corresponding work of the…

This paper introduces a novel approach to the axiomatic theory of quadratic forms. We work internally in a category of certain partially ordered sets, subject to additional conditions which amount to a strong form of local presentability.…

These Lectures are based on a course on noncommutative geometry given by the author in 2003 at the University of Chicago. The lectures contain some standard material, such as Poisson and Gerstenhaber algebras, deformations, Hochschild…

Non-vacuum exact gravitational waves invariant for a non Abelian two-dimensional Lie algebra generated by two Killing fields whose commutator is of light type, are described. The polarization of these waves, already known from previous…

We show how to define gauge-covariant coordinate transformations on a noncommuting space. The construction uses the Seiberg-Witten equation and generalizes similar results for commuting coordinates.

We discuss the noncommutative generalizations of polynomial algebras which after appropriate completions can be used as coordinate algebras in various noncommutative settings, (noncommutative differential geometry, noncommutative algebraic…

We briefly review ideas about ``noncommutativity of space-time'' and approaches toward a corresponding theory of gravity.

We review some selected aspects of the construction of gauge invariant operators in field theories on non-commutative spaces and their relation to the energy momentum tensor as well as to the non-commutative loop equations.

We compute the noncommutative deformations of a family of modules over the first Weyl algebra. This example shows some important properties of noncommutative deformation theory that separates it from commutative deformation theory.

Quantum field theories (QFT's) on noncommutative spacetimes are currently under intensive study. Usually such theories have world sheet noncommutativity. In the present work, instead, we study QFT's with commutative world sheet and…

This paper stands for an application of the noncommutative (NC) Noether theorem, given in our previous work [AIP Proc 956 (2007) 55-60], for the NC complex Grosse-Wulkenhaar model. It provides with an extension of a recent work [Physics…

For a prime $p$ and a commutative ring $R$ with unity, let $W(R)$ denote the group of $p$-typical Witt vectors. The group $W(R)$ is endowed with a Verschiebung operator $V: W(R)\to W(R)$ and a Teichm\"{u}ller map $\langle \ \rangle:…

Commutators and anticommutators of gamma matrices with arbitrary numbers of (antisymmetrized) indices are derived.