Related papers: Masaki Kashiwara and Algebraic Analysis
This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…
Colored planar rook algebra is a semigroup algebra in which the basis element has a diagrammatic description. The category of finite dimensional modules over this algebra is completely reducible and suitable functors are defined on this…
The Schwarz lemma as one of the most influential results in complex analysis and it has a great impact to the development of several research fields, such as geometric function theory, hyperbolic geometry, complex dynamical systems, and…
This is a review devoted to some results of Algebraic Programming (Computer Algebra) used in treating several problems of general relativity, based mainly on already published articles. The article contains the talk given by the author at…
We refine Osserman's argument on the exceptional values of the Gauss map of algebraic minimal surfaces. This gives an effective estimate for the number of exceptional values and the totally ramified value number for a wider class of…
The topics of Convexity and Concavity and Envelopes are central in Complex Analysis and extensively investigated. The aim of this paper is to find a possible counterpart in Algebraic Geometry. The article presents preliminary results on…
We present a differential algebra of generalized functions over a field of generalized scalars by means of several axioms in terms of general algebra and topology. Our differential algebra is of Colombeau type in the sense that it contains…
This paper surveys some applications of moduli theory to issues concerning the distribution of rational points on algebraic varieties. It will appear on the proceedings of the Fano Conference.
Meta-centralizers of non-locally compact group algebras are studied. Theorems about their representations with the help of families of generalized measures are proved. Isomorphisms of group algebras are investigated in relation with…
In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and…
Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…
The Colombeau algebra of generalized functions allows to unrestrictedly carry out products of distributions. We analyze this operation from a microlocal point of view, deriving a general inclusion relation for wave front sets of products in…
These notes are for the author's lectures, "Integral Reduction and Applied Algebraic Geometry Techniques" in the School and Workshop on Amplitudes in Beijing 2016. I introduce the applications of algebraic geometry methods on multi-loop…
In this note, we study the operation of Sasaki hook within the setting of quantum cylindric algebras by introducing cylindric quasi-implication algebras. It is first demonstrated that every quantum cylindric algebra can be converted into a…
This is a proposal of an algebra which aims at distributed array processing. The focus lies on re-arranging and distributing array data, which may be multi-dimensional. The context of the work is scientific processing; thus, the core…
We study the minus order on the algebra of bounded linear operators on a Hilbert space. By giving a characterization in terms of range additivity, we show that the intrinsic nature of the minus order is algebraic. Applications to…
The note complements topological aspects of the theory of chiral algebras.
This document contains notes from the lectures of Corti, Koll\'ar, Lazarsfeld, and Musta\c{t}\u{a} at the workshop ``Minimal and canonical models in algebraic geometry" at MSRI, Berkeley, April 2007. The lectures give an overview of the…
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
This is a review article based on a mini-course comprised of four talks given by the author at Berkeley.