Related papers: An Invitation to Noncommutative Algebra
This is the text of the lecture given by the author in Naples at "Giornata IndAM", June 7, 2005. The lecture is addressed at the general mathematical audience and reviews several topics in deformation theory of associative algebras.
We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.
These lectures given to graduate students in theoretical particle physics, provide an introduction to the ``inner workings'' of computer algebra systems. Computer algebra has become an indispensable tool for precision calculations in…
We give a rather informal introduction to the theory of mixed Hodge modules for young mathematicians.
We introduce a Hodge operator in a framework of noncommutative geometry. The complete integrability of 2-dimensional classical harmonic maps into groups (sigma-models or principal chiral models) is then extended to a class of…
A simple pedagogical introduction to the Colombeau algebra of generalised functions is presented, leading the standard definition.
This article is part introduction and part survey to the mathematical area centered around local cohomology.
Foundations of the theory of vertex algebras are extended to the non-Archimedean setting.
In this work, I investigate the noncommutative Poisson algebra of classical observables corresponding to a proposed general Noncommutative Quantum Mechanics, \cite{1}. I treat some classical systems with various potentials and some Physical…
Nongraded infinite-dimensional Lie algebras appeared naturally in the theory of Hamiltonian operators, the theory of vertex algebras and their multi-variable analogues. They play important roles in mathematical physics. This survey article…
This note highlights the key aspects of the Feichtinger algebra $\mathbf{S}_{0}(\mathbb{R})$ on the real line for non-experts.
In this paper we introduce a new invariant for a non-degenerate evolution algebra, which consists of an ordered sequence of evolution algebras of lower dimension, belonging all of them to a specific family. We use this invariant to propose…
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…
Quantum groups and quantum homogeneous spaces - developed by several authors since the 80's - provide a large class of examples of algebras which for many reasons we interpret as `coordinate algebras' over noncommutative spaces. This…
These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is…
Following the guidelines of classical differential geometry the `building material' for the tensor calculus in non-commutative geometry is suggested. The algebraic account of moduli of vectors and covectors is carried out.
The purpose of these lecture notes is to give a quick and introductory overview of holographic superconductors. Besides the actual description of the standard holographic superconductor, attention is paid to the motivations and the relation…
The article is devoted to the investigation of operators on a non locally compact group algebra. Their isomorphisms are also studied.
This survey is based on lectures given by the authors during the program "Noncommutative algebraic geometry and representation theory" at the MSRI, Berkeley, in the spring of 2013. It covers the recent work of the authors on noncommutative…