Feb. 1997
Abstract:
Let A be an algebra over a commutative ring R. We associate to R another commutative ring R and to A an R-module A. In the case where R is a field, R will be the ring of integers and A the Grothendieck group of A. In the case where A is a cellular algebra, we find elements in A which specialize to the absolutely irreducible modules of AS if R specializes to a field S. Since these span all of A, this enables us to define global decomposition numbers as elements of R. Ordinary decomposition numbers can be deduced by specializing. A is a free R-Module if and only if A is integrally quasi-hereditary. Otherwise relations can be determined explicitely. As examples, group algebras of symmetric groups over the integers are treated. They show that global decomposition numbers contain more information than the collection of all ordinary decomposition numbers.
It is possible to read this paper online.
06.03.1997, Sebastian Oehms, modifications: 05.04.1998, 20.05.2022.