scholarly journals Derived and Stable Equivalence Classification of Twisted Multifold Extensions of Piecewise Hereditary Algebras of Tree Type

2002 ◽  
Vol 249 (2) ◽  
pp. 345-376 ◽  
Author(s):  
Hideto Asashiba
Keyword(s):  
Stable Equivalence ◽  
Hereditary Algebras ◽  
Tree Type

scholarly journals Classification of Symmetric Special Biserial Algebras With At Most One Non-Uniserial Indecomposable Projective

2015 ◽  
Vol 58 (3) ◽  
pp. 739-767 ◽  
Author(s):  
Nicole Snashall ◽  
Rachel Taillefer
Keyword(s):  
Natural Generalization ◽  
Stable Equivalence ◽  
Symmetric Algebras ◽  
Special Biserial Algebras ◽  
Weakly Symmetric ◽  
Dihedral Type ◽  
Indecomposable Projective Module ◽  
Algebras Of Dihedral Type ◽  
Euclidean Type

AbstractWe consider a natural generalization of symmetric Nakayama algebras, namely, symmetric special biserial algebras with at most one non-uniserial indecomposable projective module. We describe the basic algebras explicitly by quiver and relations, then classify them up to derived equivalence and up to stable equivalence of Morita type. This includes the weakly symmetric algebras of Euclidean type n, as studied by Bocian et al., as well as some algebras of dihedral type.

scholarly journals Algebras of acyclic cluster type: Tree type and type Ã

2013 ◽  
Vol 211 ◽  
pp. 1-50 ◽  
Author(s):  
Claire Amiot ◽  
Steffen Oppermann
Keyword(s):  
Equivalence Class ◽  
Complete Classification ◽  
Global Dimension ◽  
Path Algebra ◽  
Derived Category ◽  
Derived Equivalence ◽  
Cluster Category ◽  
Cluster Type ◽  
Tree Type

AbstractIn this paper, we study algebras of global dimension at most 2 whose generalized cluster category is equivalent to the cluster category of an acyclic quiver which is either a tree or of typeÃ.We are particularly interested in their derived equivalence classification. We prove that each algebra which is cluster equivalent to a tree quiver is derived equivalent to the path algebra of this tree. Then we describe explicitly the algebras of cluster typeÃnfor each possible orientation ofÃn.We give an explicit way to read off the derived equivalence class in which such an algebra lies, and we describe the Auslander-Reiten quiver of its derived category. Together, these results in particular provide a complete classification of algebras which are cluster equivalent to tame acyclic quivers.

scholarly journals Combinatorial classification of piecewise hereditary algebras

2011 ◽  
Vol 23 (6) ◽  
Author(s):  
Marcelo Lanzilotta ◽  
Maria Julia Redondo ◽  
Rachel Taillefer
Keyword(s):  
Combinatorial Classification ◽  
Hereditary Algebras

scholarly journals Tilting modules over tame hereditary algebras

2012 ◽  
Vol 2013 (682) ◽  
pp. 1-48
Author(s):  
Lidia Angeleri Hügel ◽  
Javier Sánchez
Keyword(s):  
Complete Classification ◽  
Tilting Module ◽  
Tilting Modules ◽  
Hereditary Algebra ◽  
Infinite Dimensional ◽  
Direct Sum ◽  
Finite Dimensional ◽  
Hereditary Algebras ◽  
Tame Hereditary Algebra

Abstract. We give a complete classification of the infinite dimensional tilting modules over a tame hereditary algebra R. We start our investigations by considering tilting modules of the form where is a union of tubes, and denotes the universal localization of R at in the sense of Schofield and Crawley-Boevey. Here is a direct sum of the Prüfer modules corresponding to the tubes in . Over the Kronecker algebra, large tilting modules are of this form in all but one case, the exception being the Lukas tilting module L whose tilting class consists of all modules without indecomposable preprojective summands. Over an arbitrary tame hereditary algebra, T can have finite dimensional summands, but the infinite dimensional part of T is still built up from universal localizations, Prüfer modules and (localizations of) the Lukas tilting module. We also recover the classification of the infinite dimensional cotilting R-modules due to Buan and Krause.

scholarly journals Algebras of acyclic cluster type: Tree type and type Ã

2013 ◽  
Vol 211 ◽  
pp. 1-50 ◽  
Author(s):  
Claire Amiot ◽  
Steffen Oppermann
Keyword(s):  
Equivalence Class ◽  
Complete Classification ◽  
Global Dimension ◽  
Path Algebra ◽  
Derived Category ◽  
Derived Equivalence ◽  
Cluster Category ◽  
Cluster Type ◽  
Tree Type

AbstractIn this paper, we study algebras of global dimension at most 2 whose generalized cluster category is equivalent to the cluster category of an acyclic quiver which is either a tree or of type Ã. We are particularly interested in their derived equivalence classification. We prove that each algebra which is cluster equivalent to a tree quiver is derived equivalent to the path algebra of this tree. Then we describe explicitly the algebras of cluster type Ãn for each possible orientation of Ãn. We give an explicit way to read off the derived equivalence class in which such an algebra lies, and we describe the Auslander-Reiten quiver of its derived category. Together, these results in particular provide a complete classification of algebras which are cluster equivalent to tame acyclic quivers.

Note on the spectral classification of carbon stars in the photographic infrared region

1966 ◽  
Vol 24 ◽  
pp. 21-23
Author(s):  
Y. Fujita
Keyword(s):  
Infrared Region ◽  
Spectral Classification ◽  
Carbon Stars

We have investigated the spectrograms (dispersion: 8Å/mm) in the photographic infrared region fromλ7500 toλ9000 of some carbon stars obtained by the coudé spectrograph of the 74-inch reflector attached to the Okayama Astrophysical Observatory. The names of the stars investigated are listed in Table 1.

Diagnostic Value of Electron Microscopy in Soft Tissue Tumors

1970 ◽  
Vol 28 ◽  
pp. 220-221
Author(s):  
Gerald Fine ◽  
Azorides R. Morales
Keyword(s):  
Cardiac Myxoma ◽  
Osteogenic Sarcoma ◽  
Diagnostic Value ◽  
Soft Tissue Tumors ◽  
Amelanotic Melanoma ◽  
Growth Patterns ◽  
Light Microscopic Level ◽  
Mesenchymal Tumors ◽  
Good Agreement

For years the separation of carcinoma and sarcoma and the subclassification of sarcomas has been based on the appearance of the tumor cells and their microscopic growth pattern and information derived from certain histochemical and special stains. Although this method of study has produced good agreement among pathologists in the separation of carcinoma from sarcoma, it has given less uniform results in the subclassification of sarcomas. There remain examples of neoplasms of different histogenesis, the classification of which is questionable because of similar cytologic and growth patterns at the light microscopic level; i.e. amelanotic melanoma versus carcinoma and occasionally sarcoma, sarcomas with an epithelial pattern of growth simulating carcinoma, histologically similar mesenchymal tumors of different histogenesis (histiocytoma versus rhabdomyosarcoma, lytic osteogenic sarcoma versus rhabdomyosarcoma), and myxomatous mesenchymal tumors of diverse histogenesis (myxoid rhabdo and liposarcomas, cardiac myxoma, myxoid neurofibroma, etc.)

Ultrastructure of mesotheliomas

1984 ◽  
Vol 42 ◽  
pp. 98-101
Author(s):  
Irving Dardick
Keyword(s):  
Electron Microscopy ◽  
Latent Period ◽  
Spindle Cell ◽  
Spindle Cell Sarcoma ◽  
Metastatic Adenocarcinoma ◽  
Cell Sarcoma ◽  
Cytological Features ◽  
Industrial Use ◽  
Degree Of Differentiation

With the extensive industrial use of asbestos in this century and the long latent period (20-50 years) between exposure and tumor presentation, the incidence of malignant mesothelioma is now increasing. Thus, surgical pathologists are more frequently faced with the dilemma of differentiating mesothelioma from metastatic adenocarcinoma and spindle-cell sarcoma involving serosal surfaces. Electron microscopy is amodality useful in clarifying this problem.In utilizing ultrastructural features in the diagnosis of mesothelioma, it is essential to appreciate that the classification of this tumor reflects a variety of morphologic forms of differing biologic behavior (Table 1). Furthermore, with the variable histology and degree of differentiation in mesotheliomas it might be expected that the ultrastructure of such tumors also reflects a range of cytological features. Such is the case.

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