Generation of cohomology of graded algebras

Let A be an unital, associative, graded algebra over a base ring k. I’m happy to assume that k is a field if need be, and will insist that A free and of finite rank in each degree (locally finite). Further, A is connected: it vanishes in negative degrees and is of rank 1 (generated … Read more

Flat resolutions of DG-schemes

Recall that a DG-scheme is a pair (X,OX), where (X,O0X) is a scheme, OX is a sheaf of commutative DG-algebras over (X,O0X), and each OiX is a quasi-coherent O0X-module. I would like to know if in this generality (without assuming things like X being quasi-projective over a field of characteristic zero), is it known that … Read more

Seeking an unpublished manuscript by Tetsuro Okuyama

Several papers in representation theory attribute the notion of relatively projective modules to Tetsuro Okuyama’s manuscript “A generalization of projective covers of modules over finite group algebras.” I haven’t been able to find this by googling. Can anyone point me to a copy (or send me one)? Thanks! Answer AttributionSource : Link , Question Author … Read more

References for bilinear forms on chain complexes?

I am looking for references that include general results and theorems for bilinear forms defined on chain complexes. That is, bilinear forms ⟨⋅,⋅⟩i:Ci×Ci→K defined for all i on chain complexes ⋯→Ci+1→Ci→Ci−1→⋯ of K-modules over a principal ideal domain K. I am particularly interested in how these descend to homology groups and what invariants/classifications can be … Read more

Compactly supported distributions as a projective G-module

For a Lie group G and a locally convex space V let E(G,V) be the locally convex space of smooth functions from G to V, and accordingly E′c(G,V) the space of compactly supported distributions. A G-module V is called differentiable if v→(g→gv) defines a continuous map from V to E(G,V) for all v∈V. In particular … Read more

Universal enveloping algebra functor preserves quasi-isomorphism

Let k be a field of characteristic 0. Let DGAk denote the category of DG algebras and DGLAk denote the category of DG Lie algebras. It is well known that there are model structures on them that the weak equivalences are the quasi-isomorphisms and the fibrations are the maps which are degreewise surjective. We have … Read more

divided power structure on Hocschild cohomology?

Does Hochschild cohomology of a cocommutative Hopf algebra over a field of positive characteristic have a natural divided power structure? If not, perhaps a certain natural extra structure on the Hopf algebra would yield one? Answer AttributionSource : Link , Question Author : Roman , Answer Author : Community

Bound for the global dimension of higher Auslander algebras

Let algebras be finite dimensional and connected. Recall that an algebra A is called a higher Auslander algebra in case it the dominant dimension coincides with the global dimension and both dimension are finite and larger than or equal to two. Those algebras were introduced by Iyama as a generalisation of the classical Auslander algebras … Read more

Finitistic dimension of Nakayama algebras

Given a connected (quiver) nonselfinjective Nakayama algebra with a circle as a quiver and at least two points. Such an algebra is determined by the (Kupisch) sequence [c0,c1,…,cn−1], when the algebra has n simples and ci is the dimension of the projective module at point i. We can furthermore always rotate and assume cn−1=c0+1. Call … Read more