幻陪集分解
Magic Coset Decompositions
摘要：
利用“混合”非对称Freudenthal-Rozenfeld-Tits幻方，分析了N=2，D=4例外Maxwell-Einstein理论中作为向量多重态标量流形出现在超引力中的非紧特殊Kähler对称秩3陪集E7（-25）/[（E6（-78）× U（1））/Z3]的两种陪集分解.第一个分解具有最大的显式协方差，而第二个（试验对称）是Iwasawa型，具有最大的SO（8）协方差。对这两类陪集参数化给出了E7型单群的共形非紧实形式的推广，并讨论了它们与秩3单欧几里德若当代数和除代数上的赋范trialities的关系.
英文摘要：
By exploiting a "mixed" non-symmetric Freudenthal-Rozenfeld-Tits magic square, two types of coset decompositions are analyzed for the non-compact special Kähler symmetric rank-3 coset E7(-25)/[(E6(-78) x U(1))/Z_3], occurring in supergravity as the vector multiplets' scalar manifold in N=2, D=4 exceptional Maxwell-Einstein theory. The first decomposition exhibits maximal manifest covariance, whereas the second (triality-symmetric) one is of Iwasawa type, with maximal SO(8) covariance. Generalizations to conformal non-compact, real forms of non-degenerate, simple groups "of type E7" are presented for both classes of coset parametrizations, and relations to rank-3 simple Euclidean Jordan algebras and normed trialities over division algebras are also discussed.
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