Finiteness Conditions for the Hochschild Homology Algebra of a Commutative Algebra

Finiteness conditions on the Yoneda algebra of a monomial algebra

Let A be a connected graded noncommutative monomial algebra. We associate to A a finite graphΓ (A) called the CPS graph of A. Finiteness properties of the Yoneda algebra ExtA(k, k) including Noetherianity, finite GK dimension, and finite generation are characterized in terms of Γ (A). We show that these properties, notably finite generation, can be checked by means of a terminating algorithm. ©...

Commutative Algebra Commutative Algebra : General

On Commutative Algebra Homology in Prime Characteristics

We give decompositions of the Hochschild and cyclic homology of a com-mutative algebra in characteristic p into p?1 parts, and show these decom-positions are compatible with the shuue product structures. We also give a counterexample to a conjecture attributed to Barr, which asserts that a modiied version of Harrison cohomology coincides with Andr e/Quillen cohomology.

The Hochschild Cohomology of a Poincaré Algebra

In this note, we define the notion of a cactus set, and show that its geometric realization has a natural structure as an algebra over Voronov’s cactus operad, which is equivalent to the framed 2-dimensional little disks operad D2. Using this, we show that for a Poincaré algebra A, its Hochschild cohomology is an algebra over the (chain complexes of) D2.

Commutative Algebra

Introduction 5 0.1. What is Commutative Algebra? 5 0.2. Why study Commutative Algebra? 5 0.3. Acknowledgments 7 1. Commutative rings 7 1.1. Fixing terminology 7 1.2. Adjoining elements 10 1.3. Ideals and quotient rings 11 1.4. The monoid of ideals of R 14 1.5. Pushing and pulling ideals 15 1.6. Maximal and prime ideals 16 1.7. Products of rings 17 1.8. A cheatsheet 19 2. Galois Connections 20 2...