Abstract
10.1. Definition. [L.V. Sabinin 81, 91b] a partial left odular (diodular) space M is said to be partially symmetric if sx = (—l)x, x ∈M, is a partial automorphism of M. Note that s x,y = (Lxy)−1 x, see Chapter 1. a left (p, k)-canonical partial odular (diodular) space is said to be locally symmetric if sx = (—l)x, x ∈ M, is a Cr-smooth local automorphism of M. It is called a globally symmetric space if for any point x ∈ M there exists a global automorphism sx which coincides with sx = (—1)x whenever the latter map is defined.
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© 1999 Springer Science+Business Media Dordrecht
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Sabinin, L.V. (1999). Symmetric Geoodular Spaces. In: Smooth Quasigroups and Loops. Mathematics and Its Applications, vol 492. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4491-9_11
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DOI: https://doi.org/10.1007/978-94-011-4491-9_11
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