Let R be a left pure semisimple ring such that there are no nonzero homomorphisms from preinjective modules to non-preinjective indecomposable modules in R-mod, and let W be the left key R-module; i.e., W is the direct sum of all non-isomorphic non-preinjective indecomposable direct summands of products of preinjective left R-modules. We show that if the module W is endofinite, then R is a ring...

Let W be a finite-dimensional Z/p-module over a field, k, of characteristic p. The maximum degree of an indecomposable element of the algebra of invariants, k[W ]Z/p, is called the Noether number of the representation, and is denoted by β(W ). A lower bound for β(W ) is derived, and it is shown that if U is a Z/p submodule of W , then β(U) 6 β(W ). A set of generators, in fact a SAGBI basis, is...

1. Introduction LET 0 be a finite group. If p is a prime which, divides the order of G, there exists in general an infinite number of indecomposable representations of 0 over a field of characteristic p. We are concerned here with the in-decomposable representations of a group G which is an extension of a 2?-nilpotent"f group by a cyclic group of order prime to p. We reduce the study of these r...

Motivated by the relation between Schur algebra and group of a symmetric group, along with other similar examples in algebraic Lie theory, Min Fang Steffen Koenig [15], [16] addressed some behaviour endomorphism generator over algebra, which they called gendo-symmetric algebra. Continuing this line works, we classify article representation-finite algebras that have precisely one isomorphism cla...

We construct modules of the 0-Hecke algebra whose images under quasisymmetric characteristic map are Young row-strict Schur functions. This provides a representation-theoretic interpretation this basis functions, answering question Mason and Niese (2015). Additionally, we classify when these indecomposable.

Abstract Let k be an algebraically closed field of characteristic p > 0. We compute the Weyl filtration multiplicities in indecomposable tilting modules and decomposition numbers for general linear group over terms cap diagrams under assumption that is bigger than greatest hook length partitions involved. Then we introduce study rational Schur functor from a category GL n -modules to walled ...

For an (n − 1)-Auslander algebra Λ with global dimension n ≥ 2, we show that if Λ admits a trivial maximal (n − 1)-orthogonal subcategory of modΛ, then Λ is of finite representation type and the projective dimension or injective dimension of any indecomposable module in modΛ is at most n − 1. As a result, we have that for an Auslander algebra Λ with global dimension 2, if Λ admits a trivial max...

We say that an indecomposable Cartan matrix A with entries in the ground field of characteristic 0 is almost affine if Lie sub(super)algebra determined by it not finite dimensional or but (super)algebra any submatrix A, obtained striking out row and column intersecting on main diagonal, sum (super)algebras. said to be affine, all its matrices are affine. list superalgebras over complex numbers ...