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We describe simply connected compact exceptional simple Lie groups in very elementary way.
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F. Gantmacher · 1939
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A. Borel and J. de Siebenthal, · 1949
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Oktaven, Ausnahmegruppen und Oktavengeometry, Math. Inst. Rijkuniv. te Utrecht, 1951
H. Freudenthal, · 1951
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Some remarks on exceptional Lie group F 4 F_{4} , Nagoya Math. J. 4(1954), 83-88
Y. Matsushima, · 1954
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Y. Matsushima, · 1957
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I. Yokota, · 1959
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Beziehung der E 7 E_{7} und E 8 E_{8} zur Oktavenevene I, II, X, Nedel, Akad. Weten. Proc.Ser. A.57(1954), 218-230, 363-365, 66(1963), 457-471
H. Freudenthal, · 1963
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Clifford modules, Topology 3, Suppl. 1(1964)
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A note on S p i n ( 9 ) Spin(9) , J. Fac. Sci. Shinshu Univ. 3(1968), 61-70
I. Yokota, · 1968
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Exceptional Lie group F 4 F_{4} and its representation rings, J. Fac. Sci. Shinshu Univ. 3(1968), 35-60
I. Yokota, · 1968
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Groups and Topology (in Japanese), Shokabo, Yokyo, 1971
I. Yokota, · 1971
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A theorem on the connectedness of a subgroup of a simply connected Lie group commuting with any its automorphis
P. K. Rasevskii, · 1974
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On a non-compact simple Lie group F 4 , 1 F_{4,1} of type F 4 F_{4} , J. Fac. Sci. Shinshu Univ. 10(1975), 71-80
I. Yokota, · 1975
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Non-compat simple Lie group G 2 ′ {G_{2}}^{\prime} of type G 2 G_{2} , J. Fac. Sci. Shinshu Univ. 12(1977), 45-52
I. Yokota, · 1977
Earlier work this paper cites.
Non-compact simple Lie group F 4 , 2 F_{4,2} of type F 4 F_{4} , J. Fac. Sci. Shinshu Univ. 12(1977), 53-64
I. Yokota, · 1977
Earlier work this paper cites.
Semi-simpleLie algebras, Dekker, 1978
M. Goto and F. D. Grosshans, · 1978
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Non-compact simple Lie group E 6 ( 6 ) E_{6(6)} of type E 6 E_{6} , J. Fac. Sci. Shinshu Univ. 14(1979), 1-13
O. Shukuzawa and I. Yokota, · 1979
Cited alongside, same era.
Non-compact simple Lie group E 6 ( − 14 ) E_{6(-14)} and E 6 ( 2 ) E_{6(2)} of type E 6 E_{6} , J. Fac. Sci. Shinshu Univ. 14(1979), 15-28
O. Shukuzawa and I. Yokota, · 1979
Cited alongside, same era.
Subgroups of type A 2 A_{2} -series in the exceptional Lie group G 2 G_{2} , J. Fac. Sci. Shinshu Univ. 14(1979), 87-94
I. Yokota, · 1979
Cited alongside, same era.
Non-compacct simple Lie group E 8 ( − 24 ) E_{8(-24)} of type E 8 E_{8} , J. Fac. Sci. Shinshu Univ. 15(1980), 53-76
T. Imai and I. Yokota, · 1980
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Exceptional linear simple Lie groups (in Japaneae), Gendai-sugakusya, Kyoto, 1992
I. Yokota, · 1992
Later among the works it cites.
On the subalgebra g 0 \mbox{\es{g}}_{0} and g e v \mbox{\es{g}}_{ev} of semisimple Lie algebra, J. Math. Soc.Japan, 45(1993), 1-19
S. Kaneyuki, · 1993
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Volume formula of compact simple Lie groups and values of τ \tau , J. Fac. Sci. Shinshu Uni. 29(1994), 69-70
∗ \!\!\!{}^{*} K. Mitsuishi and I. Yokota, · 1994
Later among the works it cites.
Volumes of compact symmetric spaces, Tokyo J. Math. 20(1997), 87-105
K. Abe and I. Yokota, · 1997
Later among the works it cites.
Realization of maximal subgroups of rank 8 of the simply connected compact simple Lie group of type E 8 E_{8} , Tsukuba J. Math. 21(1997), 595-616
S. Gomyo, · 1997
Later among the works it cites.
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Simply connected compact simple Lie group E 6 ( − 78 ) E_{6(-78)} of type E 6 E_{6} and its involutive automorphisms, J. Math. Kyoto Univ. 20(1980), 447-473
† \!\!\!{}^{\dagger} I. Yokota, · 1980
Cited alongside, same era.
On bounded symmetric domains of exceptional type, J. Fac. Sci. Shinshu Univ. 16(1981), 65-96
T. Imai, · 1981
Cited alongside, same era.
Simply connected compact simple Lie group E 7 ( − 133 ) E_{7(-133)} of type E 7 E_{7} , J. Math. Kyoto Univ. 21(1981), 383-395
∗ † \!\!\!{}^{*}\,\dagger T. Imai and I. Yokota, · 1981
Cited alongside, same era.
Simply connected compact simple Lie group E 8 ( − 248 ) E_{8(-248)} of type E 8 E_{8} , J. Math. Kyoto Univ. 21(1981), 741-762
T. Imai and I. Yokota, · 1981
Cited alongside, same era.
On the homogeneous space E 8 / E 7 E_{8}/E_{7} , J. Math., Kyoto Univ. 23(1983), 467-473
I. Yokota, T, Imai and O. Yasukura, · 1983
Cited alongside, same era.
Non-compact simple Lie group E 8 ( 8 ) E_{8(8)} , Tsukuba J. Math. 10(1986), 331-349
I. Yokota and O. Yasukura, · 1986
Cited alongside, same era.
Fundamental group of semisimple symmetric spaces, Advanced Studies to pure Math. 14(1988), 519-529
J. Sekiguchi, · 1988
Cited alongside, same era.
Spinor-generators of compact exceptional Lie groups F 4 , E 6 F_{4},E_{6} and E 7 E_{7} , Tsukuba J. Math. 22(1998), 705-721
T. Miyasaka, O. Schukuzawa and I. Yokota, · 1998
Later among the works it cites.
Diagonalization of an element P P of P C \mbox{\es{P}}^{C} by the compact Lie group E 7 E_{7} , Tsukuba J. Math. 22(1998), 687-703
T. Miyasaka, O. Yasukura and I. Yokota, · 1998
Later among the works it cites.
Realizations of subgroups of type D 8 D_{8} of connected exceptional simple Lie groups of type E 8 E_{8} , Tsukuba J. Math. 23(1999), 585-615
S. Gomyo, · 1999
Later among the works it cites.
Orbit types of the compact Lie group E 7 E_{7} in the Freudenthal vector space P C \mbox{\es{P}}^{C} , Tsukuba J. Math. 23(1999), 229-234
T. Miyasaka and I. Yokota, · 1999
Later among the works it cites.
2-graded decompositions of exceptional Lie algebra g
T. Miyashita and I. Yokota, · 2000
Later among the works it cites.
Adjoint orbit types of compact exceptional Lie group G 2 G_{2} in their Lie algebra, Math. J. Okayama Univ. 43(2001), 17-180
T. Miyasaka, · 2001
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Decomposition of spinor groups by the involution σ ′ \sigma^{\prime} in exceptional Lie groups, Math. J. Okayama Univ, 44(2001), 151-158
T. Miyashita, · 2001
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Fixed points subgroups by two involutive automorphisms σ , γ \sigma,\gamma of compact exceptional Lie groups F 4 , E 6 F_{4},E_{6} and E 7 E_{7} , Tsukuba J. Math. 27(2003), 199-215
T. Miyashita, · 2003
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Diagonalization of elements of Freudenthal 𝑹 R
O. Shukuzawa, · 2003
Later among the works it cites.
Orbit space of split Freudenthal vector space, Yokohama Math. J. 50(2003), 1-10
O. Shukuzawa, · 2003
Later among the works it cites.