The cohomology ring of a monomial algebra

1994 ◽  
Vol 85 (1) ◽  
pp. 11-23 ◽  
Author(s):  
E. L. Green ◽  
D. Zacharia
Keyword(s):  
Cohomology Ring ◽  
Monomial Algebra

Finite generation of the cohomology rings for the extension algebras of monomial algebras

2022 ◽  
Author(s):  
Hongbo Shi
Keyword(s):  
Cohomology Ring ◽  
Minimal Resolution ◽  
Finitely Generated ◽  
Finite Generation ◽  
Cohomology Rings ◽  
Monomial Algebra ◽  
Monomial Algebras ◽  
Resolution Graph ◽  
Dual Extension

We describe the cohomology ring of a monomial algebra in the language of dimension tree or minimal resolution graph and in this context we study the finite generation of the cohomology rings of the extension algebras, showing among others that the cohomology ring [Formula: see text] is finitely generated [Formula: see text] is [Formula: see text] is, where [Formula: see text] is the dual extension of a monomial algebra [Formula: see text] and [Formula: see text] is the opposite algebra of [Formula: see text].

scholarly journals THE HOCHSCHILD COHOMOLOGY RING MODULO NILPOTENCE OF A MONOMIAL ALGEBRA

2006 ◽  
Vol 05 (02) ◽  
pp. 153-192 ◽  
Author(s):  
EDWARD L. GREEN ◽  
NICOLE SNASHALL ◽  
ØYVIND SOLBERG
Keyword(s):  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Finite Dimensional Algebra ◽  
Finitely Generated ◽  
Dimensional Algebra ◽  
Monomial Algebra ◽  
Hochschild Cohomology Ring ◽  
Finite Dimensional ◽  
Algebra Over A Field ◽  
The Ideal

For a finite dimensional monomial algebra Λ over a field K we show that the Hochschild cohomology ring of Λ modulo the ideal generated by homogeneous nilpotent elements is a commutative finitely generated K-algebra of Krull dimension at most one. This was conjectured to be true for any finite dimensional algebra over a field in [13].

scholarly journals The Hochschild Cohomology Ring of a Quadratic Monomial Algebra

2009 ◽  
Vol 0064 ◽  
pp. 25-26
Author(s):  
David O'Keeffe
Keyword(s):  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Monomial Algebra ◽  
Hochschild Cohomology Ring

scholarly journals The Hochschild cohomology ring modulo nilpotence of a stacked monomial algebra

2006 ◽  
Vol 105 (2) ◽  
pp. 233-258 ◽  
Author(s):  
Edward L. Green ◽  
Nicole Snashall
Keyword(s):  
Hochschild Cohomology ◽  
Cohomology Ring ◽  
Monomial Algebra ◽  
Hochschild Cohomology Ring

§ 25. The Cohomology Ring

1968 ◽  
pp. 123-132
Keyword(s):  
Cohomology Ring

A Generalization of “Concordance of PL-Homeomorphisms of Sp × Sq

1972 ◽  
Vol 24 (3) ◽  
pp. 426-431 ◽  
Author(s):  
J. P. E. Hodgson
Keyword(s):  
Equivalence Relation ◽  
Cohomology Ring

Let Mm be a closed PL manifold of dimension m. Then a concordance between two PL-homeomorphisms h0, h1:M → M is a PL-homeomorphismH: M × I → M × I such that H|M × 0 = h0 and H|M × 1 = h. Concordance is an equivalence relation and in his paper [2], M. Kato classifies PL-homeomorphisms of Sp × Sq up to concordance. To do this he treats first the problem of classifying those homeomorphisms that induce the identity in homology, and then describes the automorphisms of the cohomology ring that can arise from homeomorphisms of Sp × Sq. In this paper we show that for sufficiently connected PL-manifolds that embed in codimension 1, one can extend Kato's classification of the homeomorphisms that induce the identity in homology.

scholarly journals The existence of generating families for the cohomology ring of a graph

2003 ◽  
Vol 174 (1) ◽  
pp. 115-153 ◽  
Author(s):  
Victor Guillemin ◽  
Catalin Zara
Keyword(s):  
Cohomology Ring

The polynomial cohomology ring for characteristicp

1962 ◽  
Vol 79 (1) ◽  
pp. 297-306
Author(s):  
Robert Heaton
Keyword(s):  
Cohomology Ring

Homological Aspects of Semigroup Gradings on Rings and Algebras

1999 ◽  
Vol 51 (3) ◽  
pp. 488-505 ◽  
Author(s):  
W. D. Burgess ◽  
Manuel Saorín
Keyword(s):  
Euler Characteristic ◽  
Division Ring ◽  
Artinian Ring ◽  
Global Dimension ◽  
Monomial Algebra ◽  
Finite Dimensional ◽  
Cartan Matrices ◽  
Torsion Free ◽  
Rings And Algebras ◽  
Finite Dimensional Algebras

AbstractThis article studies algebras R over a simple artinian ring A, presented by a quiver and relations and graded by a semigroup Σ. Suitable semigroups often arise from a presentation of R. Throughout, the algebras need not be finite dimensional. The graded K0, along with the Σ-graded Cartan endomorphisms and Cartan matrices, is examined. It is used to study homological properties.A test is found for finiteness of the global dimension of a monomial algebra in terms of the invertibility of the Hilbert Σ-series in the associated path incidence ring.The rationality of the Σ-Euler characteristic, the Hilbert Σ-series and the Poincaré-Betti Σ-series is studied when Σ is torsion-free commutative and A is a division ring. These results are then applied to the classical series. Finally, we find new finite dimensional algebras for which the strong no loops conjecture holds.

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