Abstract
We investigate the set of irreducible configurations of subspaces of a Hilbert space for which the angle between every two subspaces is fixed. This is the problem of *-representations of certain algebras generated by idempotents and depending on parameters (on the set of angles). We separate the class of problems of finite and tame representation type. For these problems, we indicate conditions on angles under which the configurations of subspaces exist and describe all irreducible representations.
Similar content being viewed by others
REFERENCES
C. Davis (1958) ArticleTitleSeparation of two linear subspaces Acta Sci. Math. (Szeged) 19 172–187
P. R. Halmos (1969) ArticleTitleTwo subspaces Trans. Amer. Soc. 144 381–389
H. Wenzl (1987) ArticleTitleOn sequences of projections C. R. Math. Rep. Acad. Sci. Canada 9 IssueID1 5–9
N. Popova, “On one algebra of Temperley—Lieb type,” Proc.Math.Nat.Acad.Sci.Ukraine, 486-489 (2001).
M. Vlasenko (2004) ArticleTitleOn the growth of an algebra generated by a system of projections with fixed angles Meth. Func. Anal. Topol. 10 IssueID1 98–104
V. Ufnarovskii (1990) Combinatorial and asymptotic methods in algebra VINITI Series in Contemporary Problems in Mathematics (Fundamental Trends) VINITI Moscow 5–178
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 5, pp. 606–615, May, 2004.
Rights and permissions
About this article
Cite this article
Vlasenko, M.A., Popova, N.D. On configurations of subspaces of a Hilbert space with fixed angles between them. Ukr Math J 56, 730–740 (2004). https://doi.org/10.1007/PL00022176
Received:
Issue Date:
DOI: https://doi.org/10.1007/PL00022176