scholarly journals Hochschild cohomology commutes with adic completion

2016 ◽  
Vol 10 (5) ◽  
pp. 1001-1029 ◽  
Author(s):  
Liran Shaul
Keyword(s):  
Hochschild Cohomology ◽  
Adic Completion

scholarly journals The Gerstenhaber structure on the Hochschild cohomology of a class of special biserial algebras

2021 ◽  
Vol 580 ◽  
pp. 264-298
Author(s):  
Joanna Meinel ◽  
Van C. Nguyen ◽  
Bregje Pauwels ◽  
María Julia Redondo ◽  
Andrea Solotar
Keyword(s):  
Hochschild Cohomology ◽  
Special Biserial Algebras

scholarly journals Going from cohomology to Hochschild cohomology

2005 ◽  
Vol 288 (2) ◽  
pp. 263-278 ◽  
Author(s):  
Emil Sköldberg
Keyword(s):  
Hochschild Cohomology

scholarly journals Gerstenhaber brackets on Hochschild cohomology of twisted tensor products

2017 ◽  
Vol 11 (4) ◽  
pp. 1351-1379 ◽  
Author(s):  
Lauren Grimley ◽  
Van Nguyen ◽  
Sarah Witherspoon
Keyword(s):  
Hochschild Cohomology ◽  
Tensor Products

scholarly journals On Hochschild Cohomology of Preprojective Algebras, I

1998 ◽  
Vol 205 (2) ◽  
pp. 391-412 ◽  
Author(s):  
Karin Erdmann ◽  
Nicole Snashall
Keyword(s):  
Hochschild Cohomology ◽  
Preprojective Algebras

scholarly journals Algebra endomorphisms and derivations of some localized down-up algebras

2014 ◽  
Vol 14 (03) ◽  
pp. 1550034 ◽  
Author(s):  
Xin Tang
Keyword(s):  
Automorphism Group ◽  
Cohomology Group ◽  
Hochschild Cohomology ◽  
Root Of Unity ◽  
Hochschild Cohomology Group ◽  
Algebra Endomorphism

We study algebra endomorphisms and derivations of some localized down-up algebras A𝕊(r + s, -rs). First, we determine all the algebra endomorphisms of A𝕊(r + s, -rs) under some conditions on r and s. We show that each algebra endomorphism of A𝕊(r + s, -rs) is an algebra automorphism if rmsn = 1 implies m = n = 0. When r = s-1 = q is not a root of unity, we give a criterion for an algebra endomorphism of A𝕊(r + s, -rs) to be an algebra automorphism. In either case, we are able to determine the algebra automorphism group for A𝕊(r + s, -rs). We also show that each surjective algebra endomorphism of the down-up algebra A(r + s, -rs) is an algebra automorphism in either case. Second, we determine all the derivations of A𝕊(r + s, -rs) and calculate its first degree Hochschild cohomology group.

scholarly journals Twisted Homology of Quantum SL(2) - Part II

2009 ◽  
Vol 6 (1) ◽  
pp. 69-98 ◽  
Author(s):  
Tom Hadfield ◽  
Ulrich Krähmer
Keyword(s):  
Noncommutative Geometry ◽  
Hochschild Cohomology ◽  
Cyclic Homology ◽  
Coordinate Ring ◽  
Volume Form ◽  
Twisted Homology

AbstractWe complete the calculation of the twisted cyclic homology of the quantised coordinate ring = ℂq [SL(2)] of SL(2) that we began in [14]. In particular, a nontrivial cyclic 3-cocycle is constructed which also has a nontrivial class in Hochschild cohomology and thus should be viewed as a noncommutative geometry analogue of a volume form.

scholarly journals A Spectral Sequence for the Hochschild Cohomology of a Coconnective DGA

2013 ◽  
Vol 112 (2) ◽  
pp. 182 ◽  
Author(s):  
Shoham Shamir
Keyword(s):  
Spectral Sequence ◽  
Loop Space ◽  
Hochschild Cohomology ◽  
Derived Category ◽  
Orientable Manifold ◽  
Support Varieties ◽  
Mod P

A spectral sequence for the computation of the Hochschild cohomology of a coconnective dga over a field is presented. This spectral sequence has a similar flavour to the spectral sequence presented in [7] for the computation of the loop homology of a closed orientable manifold. Using this spectral sequence we identify a class of spaces for which the Hochschild cohomology of their mod-$p$ cochain algebra is Noetherian. This implies, among other things, that for such a space the derived category of mod-$p$ chains on its loop-space carries a theory of support varieties.

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