Projective representations. I: Projective lines over rings

DOI10.1007/BF02940921zbMath0992.51001arXiv1304.0098OpenAlexW2015277901MaRDI QIDQ5954702

Hans Havlicek, Andrea Blunck

Publication date: 16 September 2002

Published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.0098

zbMATH Keywords

projective lineprojective representationring geometry

Mathematics Subject Classification ID

Incidence structures embeddable into projective geometries (51A45) General theory of nonlinear incidence geometry (51B05) Ring geometry (Hjelmslev, Barbilian, etc.) (51C05)

Related Items (18)

Projective line over the finite quotient ring \(\text{GF}(2)[x/\langle x^{3} - x\rangle\) and quantum entanglement: theoretical background] ⋮ The groups of two by two matrices in double and dual numbers, and associated Möbius transformations ⋮ Free cyclic submodules in the context of the projective line ⋮ The shortest path problem for the distant graph of the projective line over the ring of integers ⋮ On the fine structure of the projective line over \(\text{GF(2)}\otimes\text{GF(2)}\otimes\text{GF(2)}\) ⋮ Geometries on \(\sigma\)-Hermitian matrices ⋮ Divisible designs, Laguerre geometry, and beyond ⋮ Multi-line geometry of qubit-qutrit and higher-order Pauli operators ⋮ Projective ring line encompassing two-qubits ⋮ The distant graph of the projective line over a finite ring with unity ⋮ The Cayley property of some distant graphs and relationship with the Stern-Brocot tree ⋮ A classification of the projective lines over small rings ⋮ Geometry of free cyclic submodules over ternions ⋮ Projective lines over Jordan systems and geometry of Hermitian matrices ⋮ Projective representations. II: Generalized chain geometries ⋮ Orbits of free cyclic submodules over rings of lower triangular matrices ⋮ Divisible designs from twisted dual numbers ⋮ Von Staudt's theorem revisited

Cites Work

• Neighbor-preserving homomorphisms between projective ring planes
• Spreads of right quadratic skew field extensions
• Extending the concept of chain geometry
• Klingenberg chain spaces
• Regular spreads and chain geometries
• Reguli and chains over skew fields
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