Abstract
Let E be a vector space over the division ring k and L(E) the lattice of all linear subspaces of E. If Ē is a vector space over the division ring k and T: L(E); → L(Ē) a lattice isomorphism then by the Fundamental Theorem of Projective Geometry ([1] p. 44) τ is induced by a semilinear map T: E → Ē if we assume that dim E ≥ 3.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References to Chapter IV
R. Baer, Linear Algebra and Projective Geometry. Academic Press, New York 1952.
H. Gross, On Witt’s Theorem in the Denumerably Infinite Case. Math. Ann. 170 (1967) 145–165.
H. Gross, Isomorphisms between lattices of linear subspaces which are induced by Isometries. J. Algebra 49 (1977) 537–546.
H. Gross and H.A. Keller, On the definition of Hilbert Space. manuscripta math. 23 (1977) 67–90.
C. Herrmann, On a condition sufficient for the distributivity of lattices of linear subspaces. To appear.
P. Pudlak and J. Túma, Yeast graphs and fermentation of algebraic lattices. Coll. Math. Soc. J. Bolyai, 14 (1976) Lattice Theory 301–342 ed. by A.P. Huhn and E.T. Schmidt, North Holland Publ. Company, Amsterdam.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1979 Springer Science+Business Media New York
About this chapter
Cite this chapter
Gross, H. (1979). Isomorphisms between Lattices of Linear Subspaces Which are Induced by Isometries. In: Quadratic Forms in Infinite Dimensional Vector Spaces. Progress in Mathematics, vol 1. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1454-8_5
Download citation
DOI: https://doi.org/10.1007/978-1-4757-1454-8_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-1456-2
Online ISBN: 978-1-4757-1454-8
eBook Packages: Springer Book Archive