Unitals over composition algebras

作者：Knarr Norbert^*; Stroppel Markus

来源：Forum Mathematicum, 2014, 26(3): 931-951.

DOI：10.1515/forum-2011-0139

• Moufang plane
• translation plane
• Baer involution
• polarity
• unital
• semifield
• division algebra
• alternative algebra
• composition algebra
• octonion field
• automorphism
• isomorphism
• Heisenberg group

We consider polar unitals in projective planes over composition algebras. We prove that the little projective group of such a unital is contained in the centralizer of the polarity defining the unital. This yields information about the full automorphism group of the unital; it is contained in the automorphism group of the normal subgroup generated by all translations of the unital. Over suitable ground fields (such as the real numbers) we obtain a complete description of the automorphism group of the unital in the sense that it coincides with the centralizer of the polarity. The action of a nilpotent regular normal subgroup is used to establish isomorphisms between unitals in spaces of different dimensions, and over different fields.

• 出版日期2014-5