Derived Noncommutative Deformation Theory
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Derived Noncommutative Deformation Theory
We define derived deformation theory with parameters over an operad O, and prove that the infinity-category of such theories is equivalent to the infinity-category of O!-algebras.
Noncommutative Deformation Theory
Noncommutative Deformation Theory is aimed at mathematicians and physicists studying the local structure of moduli spaces in algebraic geometry. This book introduces a general theory of noncommutative deformations, with applications to the study of moduli spaces of representations of associative algebras and to quantum theory in physics. An essential part of this theory is the study of obstructions of liftings of representations using generalised (matric) Massey products. Suitable for researchers in algebraic geometry and mathematical physics interested in the workings of noncommutative algebraic geometry, it may also be useful for advanced graduate students in these fields.
Triangulated Categories in Representation Theory and Beyond
Author: Petter Andreas Bergh
language: en
Publisher: Springer Nature
Release Date: 2024-07-29
In recent years, triangulated categories have proved very successful as a common mathematical framework for formulating important advances in various fields, and at the same time for the interaction between different subject areas. The purpose of the symposium was therefore not only the study of triangulated categories in itself, but rather fruitful exchanges between disciplines. The symposium brought together established researchers who have made important contributions involving triangulated categories. Many participants came from representation theory, but there were also participants with backgrounds in commutative algebra, geometry and algebraic topology.