Differential and integral forms on non-commutative algebras
Tomasz Brzezi\'nski
TL;DR
This paper explores algebraic methods for differentiation and integration within non-commutative geometry, providing an extended summary of a lecture course that introduces these concepts in a mathematical physics context.
Contribution
It offers a comprehensive algebraic framework for differential and integral calculus tailored to non-commutative algebras, advancing the mathematical tools in non-commutative geometry.
Findings
Develops algebraic definitions for derivatives and integrals in non-commutative settings
Connects non-commutative calculus with geometric and physical theories
Provides a pedagogical overview suitable for researchers and students
Abstract
An extended summary of the lecture course given at the V School on Geometry and Physics, Bia\l owe\.za 2016, in which an algebraic approach to differentiation and integration that is characteristic for non-commutative geometry is described.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Operator Algebra Research · Algebraic and Geometric Analysis