Noncommutative Deformation Theory

ISBN-13: 9781498796019 / Angielski / Twarda / 2017 / 242 str.

Eivind Eriksen; Olav Arnfinn Laudal; Arvid Siqveland

Opis

Deformation theory is used as a tool for studying the structure of moduli schemes in geometry by many mathematicians and physicists. Mainly, the structure of the obstruction groups and their vanishing is used for smoothness properties, but there is a need to find the structure of the singularities in moduli spaces as well. This can only be achieved by constructing the singularities, and this can be done by the deformation theory studied in this book, in particular in the study of liftings by generalized matric Massey products.

Recenzje

[Noncommutative Deformation Theory] gives both an introduction to noncommutative deformation theory, and an application of the machinery in mathematical physics. […] The material on noncommutative deformation theory and Massey products is a generalisation and combination of several papers of the authors, culminating in a clean development of a deformation theory of multiple objects in abelian categories. It is nicely explained which kinds of properties one needs to impose on the objects and the categories to mimic the results in commutative deformation theory, such as the existence of a pro-representable hull. The material on mathematical physics is based on work of the second author, and is more recent.

- Pieter Belmans, Springer Nature Review, October 2017

The book is well written, with many detailed examples, making it ideal for graduate students and mathematicians interested in the subject matter. The reviewer looks forward to future applications and developments in this important subject.

-Adam Nyman, Mathematical Reviews, May 2018

Spis treści

Classical Deformation Theory. Noncommutative Algebras and Simple Modules. Noncommutative Deformation Theory.  The Noncommutative Phase Space. A Cosmological Toy Model. Moduli of Endomorphisms of Rank Three.

O autorze

Eivind Eriksen is Associate Professor in Mathematics at BI Norwegian Business School. His research interests include noncommutative algebraic geometry, deformation theory, differential structures in algebraic geometry, and representation theory. Olav Arnfinn Laudal is Professor Emeritus in Mathematics at the University of Oslo. He has researched algebraic geometry throughout his career, and is well known for his work in deformation theory. Arvid Siqveland is Professor in Mathematics at the University College of Southeast Norway. His research interests include noncommutative algebraic geometry, deformation theory, algebraic geometry and representation theory.