Wild canonical algebras

Lenzing, Helmut; Peña, José Antonio de la

doi:10.1007/pl00004589

Cited by 57 publications

(66 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [LP2] H. Lenzing and J. A. de la Peña mention that this result also follows from results in [L1,L2,LP1] in the realm of the representation theory of certain algebras related with a weighted projective line.…”

Section: −1mentioning

confidence: 52%

McKay correspondence for the Poincaré series of Kleinian and Fuchsian singularities

Ebeling

Ploog

2009

Math. Ann.

View full text Add to dashboard Cite

show abstract

Section: −1mentioning

confidence: 52%

McKay correspondence for the Poincaré series of Kleinian and Fuchsian singularities

Ebeling

Ploog

2009

Math. Ann.

View full text Add to dashboard Cite

show abstract

“…In the form of tubular canonical algebras they provide the standard examples of tame algebras of linear growth. Up to tilting canonical algebras are characterized as the connected k-algebras with a separating exact subcategory or a separating tubular one-parameter family (see [23] and [39]). That is, the module category modΛ accepts a separating tubular family T = (T λ ) λ∈P 1 k , where T λ is a homogeneous tube for all λ with the exception of t tubes T λ 1 , .…”

Section: Proposition Let B = A/g Be a Galois Quotient Algebra Of A mentioning

confidence: 99%

“…Any pg-critical algebra is derived equivalent to an algebra of the form A((1), (1), D n ; 1), see [23].…”

Section: 7mentioning

confidence: 99%

Algebras Whose Coxeter Polynomials are Products of Cyclotomic Polynomials

Peña

2013

Algebr Represent Theor

View full text Add to dashboard Cite

Abstract. Let A be a finite dimensional algebra over an algebraically closed field k. Assume A is basic connected with n pairwise non-isomorphic simple modules. We consider the Coxeter transformation φ A as the automorphism of the Grothendieck group K 0 (A) induced by the Auslander-Reiten translation τ in the derived category Der(modA) of the module category modA of finite dimensional left A-modules. We say that A is an algebra of cyclotomic type if the characteristic polynomial χ A of φ A is a product of cyclotomic polynomials. There are many examples of algebras of cyclotomic type in the representaton theory literature: hereditary algebras of Dynkin and extended Dynkin types, canonical algebras, some supercanonical and extended canonical algebras. Among other results, we show that: (a) algebras satisfying the fractional Calabi-Yau property have periodic Coxeter transformation and are, therefore, of cyclotomic type, and (b) algebras whose homological form h A is non-negative are of cyclotomic type. For an algebra A of cyclotomic type we describe the shape of the Auslander-Reiten components of Der(modA).

show abstract

“…For many special kinds of categories, a complete description of the Auslander-Reiten components has been obtained; see, for example, [10,14,17,23,25]. For the module category of an artin algebra, a general description of these components can be found in [11,19,28].…”

Section: Introductionmentioning

confidence: 99%

Auslander-Reiten theory in a Krull-Schmidt category

Liu

2010

São Paulo J. Math. Sci.

View full text Add to dashboard Cite

Abstract. We first introduce the notion of an Auslander-Reiten sequence in a Krull-Schmidt category. This unifies the notion of an almost split sequence in an abelian category and that of an Auslander-Reiten triangle in a triangulated category. We then define the Auslander-Reiten quiver of a Krull-Schmidt category and describe the shapes of its semi-stable components. The main result generalizes those for an artin algebra and specializes to an arbitrary triangulated categories, in particular to the derived category of bounded complexes of finitely generated modules over an artin algebra of finite global dimension.

show abstract

Wild canonical algebras

Cited by 57 publications

References 24 publications

McKay correspondence for the Poincaré series of Kleinian and Fuchsian singularities

McKay correspondence for the Poincaré series of Kleinian and Fuchsian singularities

Algebras Whose Coxeter Polynomials are Products of Cyclotomic Polynomials

Auslander-Reiten theory in a Krull-Schmidt category

Contact Info

Product

Resources

About