scholarly journals The algebraic and geometric classification of nilpotent left-symmetric algebras

2021 ◽  
pp. 104287
Author(s):  
Jobir Adashev ◽  
Ivan Kaygorodov ◽  
Abror Khudoyberdiyev ◽  
Aloberdi Sattarov
Keyword(s):  
Symmetric Algebras

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 CLASSIFICATION OF GRADED LEFT-SYMMETRIC ALGEBRAIC STRUCTURES ON WITT AND VIRASORO ALGEBRAS

2011 ◽  
Vol 22 (02) ◽  
pp. 201-222 ◽  
Author(s):  
XIAOLI KONG ◽  
HONGJIA CHEN ◽  
CHENGMING BAI
Keyword(s):  
Virasoro Algebra ◽  
Indecomposable Module ◽  
Multiplication Operators ◽  
Algebraic Structures ◽  
Witt Algebra ◽  
Left Multiplication ◽  
Symmetric Algebras ◽  
Nonlinear Math ◽  
Math Phys

We find that a compatible graded left-symmetric algebraic structure on the Witt algebra induces an indecomposable module V of the Witt algebra with one-dimensional weight spaces by its left-multiplication operators. From the classification of such modules of the Witt algebra, the compatible graded left-symmetric algebraic structures on the Witt algebra are classified. All of them are simple and they include the examples given by [Comm. Algebra32 (2004) 243–251; J. Nonlinear Math. Phys.6 (1999) 222–245]. Furthermore, we classify the central extensions of these graded left-symmetric algebras which give the compatible graded left-symmetric algebraic structures on the Virasoro algebra. They coincide with the examples given by [J. Nonlinear Math. Phys.6 (1999) 222–245].

scholarly journals DERIVED EQUIVALENCE CLASSIFICATION OF SYMMETRIC ALGEBRAS OF POLYNOMIAL GROWTH

2010 ◽  
Vol 53 (2) ◽  
pp. 277-291 ◽  
Author(s):  
THORSTEN HOLM ◽  
ANDRZEJ SKOWROŃSKI
Keyword(s):  
Polynomial Growth ◽  
Derived Equivalence ◽  
Symmetric Algebras

AbstractWe complete the derived equivalence classification of all symmetric algebras of polynomial growth, by solving the subtle problem of distinguishing the standard and nonstandard nondomestic symmetric algebras of polynomial growth up to derived equivalence.

scholarly journals Derived equivalence classification of weakly symmetric algebras of Euclidean type

2004 ◽  
Vol 191 (1-2) ◽  
pp. 43-74 ◽  
Author(s):  
Rafał Bocian ◽  
Thorsten Holm ◽  
Andrzej Skowroński
Keyword(s):  
Derived Equivalence ◽  
Symmetric Algebras ◽  
Weakly Symmetric ◽  
Euclidean Type

scholarly journals EXT-FINITE MODULES FOR WEAKLY SYMMETRIC ALGEBRAS WITH RADICAL CUBE ZERO

2016 ◽  
Vol 102 (1) ◽  
pp. 108-121 ◽  
Author(s):  
KARIN ERDMANN
Keyword(s):  
Complete Classification ◽  
Finite Dimensional Algebra ◽  
Dimensional Algebra ◽  
Finite Generation ◽  
Symmetric Algebras ◽  
Finite Dimensional ◽  
Wild Representation Type ◽  
Weakly Symmetric ◽  
Support Varieties

Assume that $A$ is a finite-dimensional algebra over some field, and assume that $A$ is weakly symmetric and indecomposable, with radical cube zero and radical square nonzero. We show that such an algebra of wild representation type does not have a nonprojective module $M$ whose ext-algebra is finite dimensional. This gives a complete classification of weakly symmetric indecomposable algebras which have a nonprojective module whose ext-algebra is finite dimensional. This shows in particular that existence of ext-finite nonprojective modules is not equivalent with the failure of the finite generation condition (Fg), which ensures that modules have support varieties.

scholarly journals A classification of symmetric algebras of strictly canonical type

2009 ◽  
Vol 116 (2) ◽  
pp. 249-271 ◽  
Author(s):  
Marta Kwiecień ◽  
Andrzej Skowroński
Keyword(s):  
Symmetric Algebras ◽  
Canonical Type
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