Projective Representations I. Projective lines over rings

Abstract

We discuss representations of the projective line over a ring $R$ with 1 in a projective space over some (not necessarily commutative) field $K$. Such a representation is based upon a $(K,R)$-bimodule $U$. The points of the projective line over $R$ are represented by certain subspaces of the projective space $P(K,U\times U)$ that are isomorphic to one of their complements. In particular, distant points go over to complementary subspaces, but in certain cases, also non-distant points may have complementary images.

References in corpus (1)

• Extending the Concept of Chain Geometry

Cited by in corpus (17)

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• Projective Ring Line Encompassing Two-Qubits
• The Connected Components of the Projective Line over a Ring
• Projective Ring Line of a Specific Qudit
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• Qudits of composite dimension, mutually unbiased bases and projective ring geometry
• Radical parallelism on projective lines and non-linear models of affine spaces
• The Dual of a Chain Geometry
• Jordan homomorphisms and harmonic mappings
• From pentacyclic coordinates to chain geometries, and back
• Projective Representations II. Generalized chain geometries
• Projective lines over Jordan systems and geometry of Hermitian matrices
• On the Fine Structure of the Projective Line Over GF(2) x GF(2) x GF(2)
• The Shortest Path Problem for the Distant Graph of the Projective Line Over the Ring of Integers
• Divisible designs from twisted dual numbers
• Von Staudt's theorem revisited
• The distant graph of the projective line over a finite ring with unity