MathOverflow Operator Algebras Tag
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Research-level question-and-answer archive on MathOverflow for operator algebras, where professional mathematicians discuss C*-algebras, von Neumann algebras, K-theory and subfactors. Useful for finding references, known results and expert answers to specific technical questions once graduate-level background is in place.
More resources on Operator Algebras
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
nLab: Operator Algebra
nLab wiki entry on operator algebras, defining C*-algebras and von Neumann algebras and placing them within category theory and mathematical physics, including algebraic quantum field theory. It collects links to related entries and a curated list of standard references and lecture notes.
Noncommutative Geometry and Operator Algebras
Explore noncommutative geometry and operator algebras with Matilde Marcolli's course. Learn key concepts and applications.
Fundamentals of the Theory of Operator Algebras
Volume I of Kadison and Ringrose's graduate treatise on operator algebras, covering the functional analysis the subject needs: Banach and Hilbert spaces, bounded operators, weak topologies, then C*-algebras and the basics of von Neumann algebras. Many exercises develop the theory further.
Operator Algebras
Graduate monograph on K-theory for C*-algebras, from projections and unitaries through Bott periodicity, the six-term exact sequence, and Kasparov KK-theory. Readers learn how K-theoretic invariants classify operator algebras and connect them to topology and index theory.