We prove the Freiheitssatz for right-symmetric algebras and the decidability of the word problem for right-symmetric algebras with a single defining relation. We also prove that two generated subalgebras of free right-symmetric algebras are free and automorphisms of two generated free right-symmetric algebras are tame. Mathematics Subject Classification (2000): Primary 17A36, 17A50; Secondary 1...

In this paper, the singularity Ringel-Hall algebras are defined. A new class of perverse sheaves are shown to have purity property. The canonical bases of singularity RingelHall algebras are constructed. As an application, the existence of Hall polynomials in the tame quiver algebras is proved.

The aim of this work is to study the representation dimension cluster tilted algebras. We prove that weak tame algebras equal three. construct a generator module reaches dimension, unfortunately not always cogenerator. show for which gives dimension.

Coverings in the representation theory of algebras were introduced for the Auslander-Reiten quiver of a representation finite algebra in [15] and later for finite dimensional algebras in [2, 7, 11]. The best understood class of covering functors is that of Galois covering functors F : A → B determined by the action of a group of automorphisms of A. In this work we introduce the balanced coverin...

In continuation of the article [28] we classify all radically graded basic Hopf algebras of tame type over an algebraically closed field of characteristic 0.

space is said to be rational if its homotopy groups are rational vector spaces. Quillen has shown that up to homotopy there is a one-one correspondence between rational spaces and differential graded Lie algebras over 0. Call a two-connected space tame if the divisibility of its homotopy groups increases with dimension just quickly enough to prevent stable k-invariants from appearing. We will s...

In this paper we determine the derived representation type of quadratic string algebras and prove that every tame algebra whose quiver has cycles is equivalent to some skewed-gentle algebra.

We give a basis for the Hochschild cohomology ring of tame Hecke algebras. We then show that the Hochschild cohomology ring modulo nilpotence is a finitely generated algebra of Krull dimension 2, and describe the support varieties of modules for these algebras.