On a notion of complex Möbius gyrovector spaces

zbMath1497.46029MaRDI QIDQ2135511

Yanyan Li

Publication date: 9 May 2022

Published in: Nihonkai Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/nihonkai-mathematical-journal/volume-32/issue-2/On-a-notion-of-complex-M%c3%b6bius-gyrovector-spaces/nihmj/1643714797.full

zbMATH Keywords

Möbius gyrogroupMöbius gyrovector space

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Loops, quasigroups (20N05) Inner product spaces and their generalizations, Hilbert spaces (46C99) Nonlinear functional analysis (46T99)

Cites Work

• Finitely generated gyrovector subspaces and orthogonal gyrodecomposition in the Möbius gyrovector space
• Examples and applications of generalized gyrovector spaces
• Möbius gyrogroups: a Clifford algebra approach.
• A confirmation by hand calculation that the Möbius ball is a gyrovector space
• Extension of the unit disk gyrogroup into the unit ball of any real inner product space
• Group-like structure underlying the unit ball in real inner product spaces
• Generalized gyrovector spaces and a Mazur--Ulam theorem
• The abstract complex Lorentz transformation group with real metric. I. Special relativity formalism to deal with the holomorphic automorphism group of the unit ball in any complex Hilbert space
• Complex scalar multiplications on the Poincaré disk
• Unnamed Item

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