The symmetry algebras of Euclidean M-theory

We study the Euclidean supersymmetric D = 11 M-algebras. We consider two such D = 11 superalgebras: the first one is N = (1,1) self-conjugate complex-Hermitian, with 32 complex supercharges and 1024 real bosonic charges, the second is N = (1,0) complex-holomorphic, with 32 complex supercharges and 528 bosonic charges, which can be obtained by analytic continuation of known Minkowski M-algebra. Due to the Bott's periodicity, we study at first the generic D = 3 Euclidean supersymmetry case. The role of complex and quaternionic structures for D = 3 and D = 11 Euclidean supersymmetry is elucidated. We show that the additional 1024 - 528 = 496 Euclidean tensorial central charges are related with the quaternionic structure of Euclidean D = 11 supercharges, which in complex notation satisfy SU(2) pseudo-Majorana condition. We consider also the corresponding Osterwalder-Schrader conjugations as implying for N = (1,0) case the reality of Euclidean bosonic charges. Finally, we outline some consequences of our results, in particular for D = 11 Euclidean supergravity. (author)