The Hochschild cohomology ring modulo nilpotence of a stacked monomial algebra
Edward L. Green ; Nicole Snashall
Colloquium Mathematicae, Tome 106 (2006), p. 233-258 / Harvested from The Polish Digital Mathematics Library
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This paper studies the Hochschild cohomology of finite-dimensional monomial algebras. If Λ = K/I with I an admissible monomial ideal, then we give sufficient conditions for the existence of an embedding of K[x₁,...,xr]/⟨xaxbfora≠b⟩ into the Hochschild cohomology ring HH*(Λ). We also introduce stacked algebras, a new class of monomial algebras which includes Koszul and D-Koszul monomial algebras. If Λ is a stacked algebra, we prove that HH*(Λ)/≅K[x₁,...,xr]/⟨xaxbfora≠b⟩, where is the ideal in HH*(Λ) generated by the homogeneous nilpotent elements. In particular, this shows that the Hochschild cohomology ring of Λ modulo nilpotence is finitely generated as an algebra.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:283874 
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     author = {Edward L. Green and Nicole Snashall},
     title = {The Hochschild cohomology ring modulo nilpotence of a stacked monomial algebra},
     journal = {Colloquium Mathematicae},
     volume = {106},
     year = {2006},
     pages = {233-258},
     zbl = {1110.16008},
     language = {en},
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Edward L. Green; Nicole Snashall. The Hochschild cohomology ring modulo nilpotence of a stacked monomial algebra. Colloquium Mathematicae, Tome 106 (2006) pp. 233-258. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-2-6/