On the Multiplicity Problem and the Isomorphism Problem for the Four Subspace Algebra

Abstract

Let Λ be the four subspace algebra. We show that for any Λ-module M there exists an algorithm (up to the problem of finding roots of the so-called characteristic polynomial of M) with relatively low polynomial complexity of determining multiplicities of all direct summands of M. Moreover, we give a fully algorithmic criterion for deciding if two Λ-modules M and N are isomorphic.

Key Words:

• Four subspace problem
• Isomorphism problem
• Multiplicity problem

2010 Mathematics Subject Classification:

• 15A21
• 15A22
• 16G20
• 16G70
• 68Q99

ACKNOWLEDGMENT

The author was supported by the Research Grant N N201 542138 of the Polish Ministry of Science and Higher Education.

Notes

The proofs for all cases are available at the web address http://www-users.mat.umk.pl/ ∼izydor/prace/Proposition3.3.pdf

Communicated by D. Zacharia.