**Deformations of Algebras in Noncommutative Geometry**

by Travis Schedler

**Publisher**: arXiv 2015**Number of pages**: 120

**Description**:

In these notes, we give an example-motivated review of the deformation theory of associative algebras in terms of the Hochschild cochain complex as well as quantization of Poisson structures, and Kontsevich's formality theorem in the smooth setting. We then discuss quantization and deformation via Calabi-Yau algebras and potentials.

Download or read it online for free here:

**Download link**

(1.1MB, PDF)

## Similar books

**Geometric Models for Noncommutative Algebra**

by

**Ana Cannas da Silva, Alan Weinstein**-

**University of California at Berkeley**

Noncommutative geometry is the study of noncommutative algebras as if they were algebras of functions on spaces, like the commutative algebras associated to affine algebraic varieties, differentiable manifolds, topological spaces, and measure spaces.

(

**7447**views)

**Noncommutative Geometry**

by

**Alain Connes**-

**Academic Press**

The definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics. Ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics.

(

**10845**views)

**Homological Methods in Noncommutative Geometry**

by

**D. Kaledin**

The first seven lectures deal with the homological part of the story (cyclic homology, its various definitions, various additional structures it possesses). Then there are four lectures centered around Hochschild cohomology and the formality theorem.

(

**6939**views)

**Noncommutative Geometry, Quantum Fields and Motives**

by

**Alain Connes, Matilde Marcolli**-

**American Mathematical Society**

The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role.

(

**9787**views)