Support Varieties and Hochschild Cohomology Rings

By N. Snashall, Ø. Solberg. 2004

172 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3c24a5e5e820d8a92e58b46c74510924b70aa14c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. S. Iyengar
2. Henning Krause
3. D. Benson
4. L. Avramov
5. J. Pevtsova
6. Ryo Takahashi
7. R. Taillefer
8. N. Snashall

In Geometry and Topology

1. S. Iyengar
2. Henning Krause
3. D. Benson
4. L. Avramov
5. Ryo Takahashi
6. J. Pevtsova
7. S. Witherspoon
8. R. Taillefer

In Mathematical Physics

1. S. Iyengar
2. Henning Krause
3. D. Benson
4. J. Pevtsova
5. L. Avramov
6. S. Witherspoon
7. R. Taillefer
8. N. Snashall

Citations in the corpus

• MULTIPLICATIVE STRUCTURES FOR KOSZUL ALGEBRAS (2005, background): “This can be seen by noting that the kernel of φΛ/r is contained in the ideal generated by homogeneous nilpotent elements [16].”
• The hochschild cohomology ring of a class of special biserial algebras (2008, background): “As a consequence the conjecture of [18], concerning the Hochschild cohomology ring modulo nilpotence, holds for this class of algebras.”
• Local cohomology and support for triangulated categories (2007, background): “Generalizing the theory for finite groups, there is a theory of support varieties for modules over a finite dimensional algebra A, developed by Snashall and Solberg [52]; see also Solberg [53].”
• Support varieties: an ideal approach (2005, background): “ product is not necessarily commutative. This category can be used to define support varieties of representations of finite dimensional algebras, generalizing the classical case of a group algebra; see [16] Example 9.6. Let A be a finite dimensional algebra over a field k and let Ae = A⊗k Aop be its env”
• Constructing modules with prescribed cohomological support (2007, background): “Parallel theories have been constructed for finitely generated modules over finite dimensional self-injective algebras, [12, 22], and over local complete intersection rings, [1, 2].”
• Varieties for Modules of Quantum Elementary Abelian Groups (2006, methodology): “We now explain the connection between our results and the work on support varieties which was done from the point of view of Hochschild cohomology in [13], [14], [29].”