The Hochschild cohomology ring modulo nilpotence of a stacked monomial algebra

Edward L. Green; Nicole Snashall

Colloquium Mathematicae (2006)

  • Volume: 105, Issue: 2, page 233-258
  • ISSN: 0010-1354

Abstract

top
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 [ x ₁ , . . . , x r ] / ⟨ x a x b f o r a ≠ 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 H H * ( Λ ) / ≅ K [ x ₁ , . . . , x r ] / ⟨ x a x b f o r a ≠ 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.

How to cite

top

Edward L. Green, and Nicole Snashall. "The Hochschild cohomology ring modulo nilpotence of a stacked monomial algebra." Colloquium Mathematicae 105.2 (2006): 233-258. <http://eudml.org/doc/283874>.

@article{EdwardL2006,
abstract = {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 $K[x₁,..., x_r]/⟨x_ax_b for a ≠ b⟩$ 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 $HH*(Λ)/ ≅ K[x₁,..., x_r]/⟨x_ax_b for a ≠ b⟩$, 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.},
author = {Edward L. Green, Nicole Snashall},
journal = {Colloquium Mathematicae},
keywords = {stacked monomial algebras; -Koszul algebras; Hochschild cohomology rings; nilpotent elements.},
language = {eng},
number = {2},
pages = {233-258},
title = {The Hochschild cohomology ring modulo nilpotence of a stacked monomial algebra},
url = {http://eudml.org/doc/283874},
volume = {105},
year = {2006},
}

TY - JOUR
AU - Edward L. Green
AU - Nicole Snashall
TI - The Hochschild cohomology ring modulo nilpotence of a stacked monomial algebra
JO - Colloquium Mathematicae
PY - 2006
VL - 105
IS - 2
SP - 233
EP - 258
AB - 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 $K[x₁,..., x_r]/⟨x_ax_b for a ≠ b⟩$ 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 $HH*(Λ)/ ≅ K[x₁,..., x_r]/⟨x_ax_b for a ≠ b⟩$, 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.
LA - eng
KW - stacked monomial algebras; -Koszul algebras; Hochschild cohomology rings; nilpotent elements.
UR - http://eudml.org/doc/283874
ER -

NotesEmbed ?

top

You must be logged in to post comments.