representations of posets / almost completely decomposable groups

• Applicant: Professor Dr. Otto Mutzbauer
• Subject Area: Mathematics
• Term: from 2014 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 256279335

We consider representations of posets, more precisely of inverted forests over the integers modulo a prime power, and investigate if there are only finitely many or infinitely many indecomposable representations. We speak of primary representations and of bounded or unbounded,There is a 1-1-translation of this problem into the theory of almost completely decomposable (abelian) groups with the given poset as critical typeset a and regulator quotient of prime power exponent. All subclasses have to be determined to be bounded or unbounded, i.e., if there are finitely or infinitely many isomorphism types of indecomposables. This question, eventually, is a matrix problem, and there are well-developed techniques.The restrictions "inverted forest" and "integers modulo a prime power" are due to group theory. Without those restrictions there is, at the moment, no idea how to proceed.There are only finitely many bounded subclasses, the infinite rest is unbounded. At present only four, of the originally about 20 subclasses, are unknown to be bounded or not. Closing this gap the indicated problem is totally solved. To finish this theory is our intention, a group of four scientists. At the moment only our team is active in this topic and we are well-prepared. If we, our team, don't solve this problem in the very near future, this theory probably will stay incomplete for a long time.

• DFG Programme: Research Grants
• International Connection: Turkey, USA
• Cooperation Partners: Professor Dr. David Arnold; Professor Dr. Adolf Mader; Professorin Dr. Ebru Solak