Support varieties over skew complete intersections via derived braided Hochschild cohomology. (English) Zbl 1498.13043
The authors study skew complete intersection rings by adjusting techniques from the study of commutative complete intersection rings. A skew complete intersection ring is a quotient of a skew polynomial ring by an ideal generated by a regular sequence of normal elements. By putting a ‘color grading’ on the ring, the authors are able to control the non-commutativity. This allows for a description of the braided Hochschild cohomology, cohomological operators, and support varieties. Many results for commutative complete intersection rings also hold for skew complete intersection rings: Finiteness of Ext modules over the ring of cohomological operators, vanishing of Ext modules, and the generalized Auslander-Reiten conjecture, among others.
Reviewer: Janina C. Letz (Bielefeld)
MSC:
| 13D03 | (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) |
| 16E65 | Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) |
| 16E40 | (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) |
| 16E30 | Homological functors on modules (Tor, Ext, etc.) in associative algebras |
| 16E05 | Syzygies, resolutions, complexes in associative algebras |
| 16E45 | Differential graded algebras and applications (associative algebraic aspects) |
| 13D07 | Homological functors on modules of commutative rings (Tor, Ext, etc.) |
| 18G80 | Derived categories, triangulated categories |
Keywords:
skew complete intersection; complete intersection; braided Hochschild cohomology; support variety; color DG algebraReferences:
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