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This Concept Map, created with IHMC CmapTools, has information related to: Basic notions behind M^8-H duality.cmap, THE BASIC NOTIONS BEHIND M^8-H DUALITY 1. a) Quaternionic (associative) 4- plane of 8-D octonionic space O containing preferred complex plane E^2 b) Co-quaternionic (co-associative) 4-plane of O: now orthogonal comple- ment is quaternionic and contains prefer- red complex plane E^2, THE BASIC NOTIONS BEHIND M^8-H DUALITY 2. The space of quaternionic planes of O containing a fixed complex plane E^2 is parametrized by CP_2, THE BASIC NOTIONS BEHIND M^8-H DUALITY 4. a) complex (commutative) 4-surface in O has at each point com- plex plane con- taining fixed com- plex plane E^2. b) Co-complex (co-associative) 2-surface is defined analogously. c) The generaliza- tion Minkwoskian situation is obvious using hyper-complex numbers, The space of quaternionic planes of O containing a fixed complex plane E^2 is parametrized by CP_2 generalizing to co-associative context: now normal planes containing fixed E^2 are parametrized by CP_2, THE BASIC NOTIONS BEHIND M^8-H DUALITY 3. a) quaternionic (associative) 4-surface in O has at each point quaternionic plane containing fixed complex plane E^2. b) Co-quaternionic (co-associative) 4-surface is defined analogously
