For a prime number p, we construct a generating set for the ring of invariants for the p+1 dimensional indecomposable modular representation of a cyclic group of order p. We then use the constructed invariants to describe the decomposition of the symmetric algebra as a module over the group ring, confirming the Periodicity Conjecture of Ian Hughes and Gregor Kemper for this case.

The left part LA of the module category of an artin algebra A consists of all indecomposables whose predecessors have projective dimension at most one. In this paper, we study the Auslander-Reiten components of A (and of its left support Aλ) which intersect LA and also the class E of the indecomposable Ext-injectives in the addditive subcategory addLA generated by LA.

In this paper we study the category C of finite–dimensional representations of affine Lie algebras. The irreducible objects of this category were classified and described explicitly in [2],[4]. It was known however that C was not semisimple. In such a case a natural problem is to describe the blocks of the category. The blocks of an abelian category are themselves abelian subcategories, each of...

We give a complete classification of infinite dimensional indecomposable weight modules over the Lie superalgebra sl(2/1). §1. Introduction Among the basic-classical Lie superalgebras classified by Kac [3], the lowest dimensional of these is the Lie superalgebra B(0, 1) or osp(1, 2), while the lowest dimensional of these which has an isotropic odd simple root is the Lie superalgebra A(1, 0) or ...

Let A be a finitary algebra over a finite field k, and A-mod the category of finite dimensional left A-modules. Let H(A) be the corresponding Hall algebra, and for a positive integer r let Dr(A) be the subspace of H(A) which has a basis consisting of isomorphism classes of modules in A-mod with at least r+1 indecomposable direct summands. If A is hereditary of type An, then Dr(A) is known to be...

Let G be a semisimple affine algebraic group of inner type over a field F . We write XG for the class of all finite direct products of projective G-homogeneous F varieties. We determine the structure of the Chow motives with coefficients in a finite field of the varieties in XG. More precisely, it is known that the motive of any variety in XG decomposes (in a unique way) into a sum of indecompo...

Abstract Let R be a discrete valuation domain with field of fractions Q and maximal ideal generated by $\pi $ . $\Lambda an -order such that $Q\Lambda is separable -algebra. Maranda showed there exists $k\in \mathbb {N}$ for all -lattices L M , if $L/L\pi ^k\simeq M/M\pi ^k$ then $L\simeq M$ Moreover, complete indecomposable -lattice, also indecomposable. We extend Maranda’s theorem to the clas...

Let F be an arbitrary field. Let A be a central simple F -algebra. Let G be the algebraic group AutA of automorphisms of A. Let XA be the class of finite direct products of projective G-homogeneous F -varieties (the class XA includes the generalized Severi-Brauer varieties of the algebra A). Let p be a positive prime integer. For any variety in XA, we determine its canonical dimension at p. In ...

We consider critical dense polymers L(1, 2). We obtain for this model the eigenvalues of the local integrals of motion of the underlying Conformal Field Theory by means of Thermodynamic Bethe Ansatz. We give a detailed description of the relation between this model and Symplectic Fermions including some examples of the indecomposable structure of the transfer matrix in the continuum limit. Inte...