The Hochschild cohomology ring modulo nilpotence of a stacked monomial algebra

• Autorzy: Edward L. Green , Nicole Snashall
• Języki publikacji: EN

Abstrakty

EN

This paper studies the Hochschild cohomology of finite-dimensional monomial algebras. If Λ = K𝓠/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 $HH*(Λ)/𝓝 ≅ K[x₁,..., x_r]/⟨x_ax_b for a ≠ b⟩$, where 𝓝 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.

Kategorie tematyczne

• 16S15: Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
• 16G20: Representations of quivers and partially ordered sets
• 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 105
• Numer: 2
• Strony: 233-258

Daty

wydano

2006

Twórcy

autor

Edward L. Green

• Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123, U.S.A.

autor

Nicole Snashall

• Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, England

Identyfikatory

DOI

10.4064/cm105-2-6