Lectures on Noncommutative Geometry
By V. Ginzburg. 2005
109 citations recorded by the source corpus.
These Lectures are based on a course on noncommutative geometry given by the author in 2003 at the University of Chicago. The lectures contain some standard material, such as Poisson and Gerstenhaber algebras, deformations, Hochschild cohomology, Serre functors, etc. We also discuss many less known as well as some new results, in particular, noncommutative Chern-Weil theory, noncommutative symplectic geometry, noncommutative differential forms and double-tangent bundles.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/002cd3d56f6a888be7cf684d400356743a05ea76
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In Geometry and Topology
- V. Ginzburg
- Volodymyr Mazorchuk
- Pavel Etingof
- Markus Reineke
- C. Stroppel
- I. Losev
- W. Crawley‐Boevey
- I. Gordon
In Mathematical Physics
- Volodymyr Mazorchuk
- C. Stroppel
- Pavel Etingof
- V. Ginzburg
- I. Losev
- Markus Reineke
- W. Crawley‐Boevey
- D. Shklyarov
Citations in the corpus
- Projective-injective modules, Serre functors and symmetric algebras (2005, background): “Because of this result and [32], Proposition 20.”
- Moduli of representations of quivers (2008, result): “th Hochschild homology HH 0(kQ) equals kQ/[kQ,kQ], the path algebra modulo additive commutators, an object which plays a central role in some approaches to noncommutative algebraic geometry (see e.g. [26]). Now HH 0(kQ) inherits a NI-grading from kQ, and the degree d-part has a basis consisting of c”
- Noncommutative geometry and quiver algebras (2005, background): “e Q, the map Ψ becomes an isomorphism of (finite dimensional) vector spaces. We now resume the proof of part (ii) of the Theorem. The implication Ais smooth =⇒ Rep(A,V) is smooth is standard, cf. e.g. [Gi3]. Next, fix ρ∈ Rep(A,V), view V = Vρ as a left A-module and view Endk Vρ as an A-bimodule. We pu”
- Positive scalar curvature on foliations (2015, background): “This new proof provides a positive answer to a long-standing question in index theory (cf. [16, p. 5 of Lecture 9]).”
- Mirror symmetry: from categories to curve counts (2015, unknown): “Proof See e.g., [Gin05, Prop.”
- Hirzebruch–Riemann–Roch‐type formula for DG algebras (2007, background): “ements of a DG analog of the matrix algebra Mat(A), π[α|...|α] is an element of the Hochschild chain complex of this DG matrix algebra, and str is an analog of the usual trace map tr : Mat(A) →A (see [24, 43]). Note that α is upper-triangular, so the series terminates. To present our next result, we”