Generic modules have been introduced by Crawley-Boevey in order to provide a better understanding of nite dimensional algebras of tame representation type. In fact he has shown that the generic modules correspond to the one-parameter families of indecomposable nite dimensional modules over a tame algebra 5]. The Second Brauer-Thrall Conjecture provides another reason to study generic modules be...

Let A be a finite-dimensional, basic, connected algebra over an algebraically closed field. Denote by Γ (A) the Auslander–Reiten quiver of A. We show that A is representation-finite if and only if Γ (A) has at most finitely many vertices lying on oriented cycles and finitely many orbits with respect to the action of the Auslander–Reiten translation. Let K denote a fixed algebraically closed fie...

An artin algebra A over a commutative artin ring R is called quasitilted if gl.dimA ≤ 2 and for each indecomposable finitely generated A-module M we have pdM ≤ 1 or idM ≤ 1. In [11] several characterizations of quasitilted algebras were proven. We investigate the structure and homological properties of connected components in the Auslander–Reiten quiver ΓA of a quasitilted algebra A. Let A be a...

Let k be an algebraically closed field of characteristic 0 or p>2. G affine supergroup scheme over k. We classify the indecomposable exact module categories tensor category sCohf(G) (coherent sheaves of) finite dimensional O(G)-supermodules in terms (H,Ψ)-equivariant coherent on G. deduce from it classification geometrical sRep(G). When is finite, this yields all In particular, we obtain a twis...

We investigate a class of Lie algebras called quasi-simple Lie algebras. These are generalizations of semi-simple, reductive, and affine Kac-Moody Lie algebras. A quasi-simple Lie algebra which has an irreducible root system is said to be irreducible and we note that this class of algebras have been under intensive investigation in recent years. They have also been called extended affine Lie al...

The representation type of tensor product algebras of finite-dimensional algebras is considered. The characterization of algebras A, B such that A⊗B is of tame representation type is given in terms of the Gabriel quivers of the algebras A, B. Introduction. In this paper by an algebra we mean a finite-dimensional algebra over a fixed algebraically closed field K. All algebras are assumed to be b...

Let (W,S) be a finite Coxeter system. Tits defined an associative product on the set Σ of simplices of the associated Coxeter complex. The corresponding semigroup algebra is the Solomon-Tits algebra of W . It contains the Solomon algebra of W as the algebra of invariants with respect to the natural action of W on Σ. For the symmetric group Sn, there is a 1-1 correspondence between Σ and the set...

Let C be a finite braided multitensor category. Then the end B=∫X∈CX⊗X⁎ is natural Hopf algebra in C. We show that Drinfeld center of isomorphic to category left B-comodules C, and decomposition B into direct sum indecomposable C-subcoalgebras leads B-ComodC C-module subcategories. As an application, we present explicit characterization structure irreducible Yetter-Drinfeld modules over semisim...

Theory of matrix factorizations is useful to study hypersurfaces in commutative algebra. To noncommutative hypersurfaces, which are important objects algebraic geometry, we introduce a notion factorization for an arbitrary nonzero non-unit element ring. First show that the category graded invariant under operation called twist (this result generalization by Cassidy-Conner-Kirkman-Moore). Then g...

Boolean algebras have an exceptionally rich and smooth structure theory, of which Stone’s representation theorem is a prominent example. What is so special about Boolean algebras that is responsible for this nice behaviour? Given a similarity type ν, can we always find a class of algebras of type ν that displays Boolean-like features? And what does it mean, for an algebra of a given type ν that...