by Hua, Jiuzhao; Xiao, Jie

In this paper, the double Ringel–Hall algebras of tame hereditary algebras are decomposed as the quantized enveloping algebras of the infinite-dimensional Lie algebras, which are the central extensions of the affine loop algebras and the infinite-dimensional Heisenberg algebras. The numbers of the generators of the Heisenberg algebras are explicitly given at each dimensional level.

DOI: 10.1023/A:1020566614589
Print publication date: 12/1/2002
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by Natale, Sonia

We conclude the classification of Hopf algebras of dimension 12 over an algebraically closed field of characteristic zero.

DOI: 10.1023/A:1020504123567
Print publication date: 12/1/2002
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by Erdmann, Karin; Holm, Thorsten; Snashall, Nicole

Up to derived equivalence, the representation-finite self-injective algebras of class A
_n are divided into the wreath-like algebras (containing all Brauer tree algebras) and the Möbius algebras. In Part I (Forum Math.
(1999), 177–201), the ring structure of Hochschild cohomology of wreath-like algebras was determined, the key observation being that kernels in a minimal bimodule resolution of the algebras are twisted bimodules. In this paper we prove that also for Möbius algebras certain kernels in a minimal bimodule resolution carry the structure of a twisted bimodule. As an application we obtain detailed information on subrings of the Hochschild cohomology rings of Möbius algebras.

DOI: 10.1023/A:1020551906728
Print publication date: 12/1/2002
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by Beligiannis, Apostolos

Our aim in this paper is to develop a theory of purity and to prove in a unified conceptual way the existence of almost split morphisms, almost split sequences and almost split triangles in abstract homotopy categories, a rather omnipresent class of categories of interest in representation theory. Our main tool for doing this is the classical Brown representability theorem.

DOI: 10.1023/A:1020535022658
Print publication date: 12/1/2002
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by

DOI: 10.1023/A:1020599109684
Print publication date: 12/1/2002
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