The Φ-group for n submodules systems as a generalization of the K-theory

Abstract

In this paper, the authors construct a Φ-group for n submodules, which generalizes the classical K-theory and gives more information than the classical ones. This theory is related to the classification theory for indecomposable systems of n subspaces.

Keywords

System of n subspaces / System of n submodules / Φ-Group / K-Theory / Indecomposable system

References

[1] Gelfand I M, Ponomarev V A. Problems of linear algebra and classification of quadruples of subspaces in a finite-dimensional vector space. Coll. Math. Spc. Bolyai, 1970, 5: 163-237

[2] Moskaleva Y P, Samoĭlenko Y S. Systems of n subspaces and representation of *-algebras generated by projections. Methods of Functional Analysis and Topology, 2006, 12(1): 57-73

[3] Enomoto M, Watatani Y. Relative position of four subspaces in a Hilbert space. Advances in Mathematics, 2006, 201(2): 263-317

[4] Rørdam M, Larsen F, Laustsen N. An Introduction to K-Theory for C*-Algebras, 2000, London: Cambridge University Press

[5] Ostrovskyĭ Vasyl L, Samoĭlenko Y S. On pairs of self-adjoint operators. Seminar Sophus Lie, 1993, 3: 185-218