DERIVED EQUIVALENCE CLASSIFICATION OF SYMMETRIC ALGEBRAS OF POLYNOMIAL GROWTH

Abstract We 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.

[1]  D. Al-Kadi Distinguishing derived equivalence classes using the second Hochschild cohomology group , 2009, 0912.2971.

[2]  A. Zimmermann,et al.  Generalized Reynolds ideals and derived equivalences for algebras of dihedral and semidihedral type , 2008, 0807.0688.

[3]  Gizem Karaali Book Review: Elements of the Representation Theory of Associative Algebras 2: Tubes and Concealed Algebras of Euclidean Type , 2008 .

[4]  Gizem Karaali Book Review: Elements of the Representation Theory of Associative Algebras 3: Representation-Infinite Tilted Algebras , 2008 .

[5]  K. Erdmann,et al.  Deformed preprojective algebras of generalized Dynkin type , 2007 .

[6]  A. Zimmermann INVARIANCE OF GENERALISED REYNOLDS IDEALS UNDER DERIVED EQUIVALENCES , 2005, Mathematical Proceedings of the Royal Irish Academy.

[7]  D. Simson,et al.  Tubes and concealed algebras of Euclidean type , 2007 .

[8]  Daniel Simson,et al.  Elements of the Representation Theory of Associative Algebras: Techniques of Representation Theory , 2006 .

[9]  K. Erdmann,et al.  The stable Calabi-Yau dimension of tame symmetric algebras , 2006 .

[10]  A. Skowroński Selfinjective algebras: finite and tame type , 2006 .

[11]  T. Holm,et al.  Derived equivalence classification of symmetric algebras of domestic type , 2005, math/0511227.

[12]  J. Murray,et al.  Central ideals and Cartan invariants of symmetric algebras , 2005 .

[13]  T. Holm,et al.  Derived Equivalence Classification of Nonstandard Selfinjective Algebras of Domestic Type , 2005, math/0507433.

[14]  T. Holm,et al.  Derived equivalence classification of weakly symmetric algebras of Euclidean type , 2004 .

[15]  J. Białkowski,et al.  Socle deformations of selfinjective algebras of tubular type , 2004 .

[16]  T. Holm,et al.  Derived equivalences for tame weakly symmetric algebras having only periodic modules , 2003 .

[17]  Takayoshi Wakamatsu On Frobenius algebras , 2003 .

[18]  J. Białkowski,et al.  On tame weakly symmetric algebras having only periodic modules , 2003 .

[19]  T. Holm,et al.  On nonstandard tame selfinjective algebras having only periodic modules , 2003 .

[20]  H. Krause,et al.  Stable Equivalence and Generic Modules , 2000 .

[21]  H. Asashiba,et al.  The Derived Equivalence Classification of Representation-Finite Selfinjective Algebras , 1999 .

[22]  T. Holm Derived Equivalence Classification of Algebras of Dihedral, Semidihedral, and Quaternion Type , 1999 .

[23]  Jeremy Rickard,et al.  Derived Equivalences As Derived Functors , 1991 .

[24]  B. Külshammer Group-theoretical descriptions of ring-theoretical invariants of group algebras , 1991 .

[25]  A. Schofield TRIANGULATED CATEGORIES IN THE REPRESENTATION THEORY OF FINITE DIMENSIONAL ALGEBRAS (London Mathematical Society Lecture Note Series 119) , 1990 .

[26]  K. Erdmann Blocks of Tame Representation Type and Related Algebras , 1990 .

[27]  J. Rickard Derived categories and stable equivalence , 1989 .

[28]  A. Skowronski Selfinjective algebras of polynomial growth , 1989 .

[29]  Jeremy Rickard,et al.  Morita Theory for Derived Categories , 1989 .

[30]  A. Skowroński,et al.  Polynomial growth trivial extensions of simply connected algebras , 1989 .

[31]  Dieter Happel,et al.  Triangulated categories in the representation theory of finite dimensional algebras , 1988 .

[32]  Dieter Happel,et al.  On the derived category of a finite-dimensional algebra , 1987 .

[33]  C. Ringel,et al.  The derived category of a tubular algebra , 1986 .

[34]  Burkhard Külshammer Bemerkungenüber die Gruppenalgebra als symmmetrische Algebra, II , 1982 .

[35]  Burkhard Külshammer,et al.  Bemerkungen über die gruppenalgebra als symmetrische Algebra, III , 1981 .

[36]  Ju. A. Drozd,et al.  Tame and wild matrix problems , 1980 .

[37]  Murray Gerstenhaber,et al.  The Cohomology Structure of an Associative Ring , 1963 .

[38]  中山 正 On frobeniusean algebras , 1941 .