Invariant lattices of type \(F_ 4\) and \(E_ 6\): The automorphism groups. (English) Zbl 0788.17007
The authors describe automorphism groups for all invariant lattices of types \(F_ 4\) and \(E_ 6\). The proofs of the main results are based on the classification of finite simple groups.
Reviewer: K.Riives (Tartu)
References:
| [1] | Abdukhalikov K.S., Math. USSR Sbornik |
| [2] | Alekseevsky A.V., Funct. Anal. Appl 8 pp 277– (1974) · Zbl 0307.22008 · doi:10.1007/BF01075483 |
| [3] | ATLAS of finite groups (1988) |
| [4] | Bondal A.I., Math. USSR Sbornik 58 pp 735– (1987) · Zbl 0634.10028 · doi:10.1070/SM1987v058n02ABEH003113 |
| [5] | Borovik A.V., Algebra and Logic 28 (3) pp 163– (1989) · Zbl 0719.20025 · doi:10.1007/BF01978721 |
| [6] | Burichenko V.P., Moscow Univ. Math. Bull 43 (4) pp 74– (1988) |
| [7] | Burichenko V.P., Mat. Sbornik 182 (10) (1991) |
| [8] | Cohen A.M., Proc. Symp. Pure Math 47 (10) pp 367– (1987) · doi:10.1090/pspum/047.2/933426 |
| [9] | Cohen A.M., Proc. London Math.Soc 64 (10) pp 21– (1992) · Zbl 0706.20037 · doi:10.1112/plms/s3-64.1.21 |
| [10] | Cooperstein B.N., II, Geom. Dedicata 15 (10) pp 1– (1983) |
| [11] | Fischer B., Invent. Math 13 (10) pp 232– (1971) · Zbl 0232.20040 · doi:10.1007/BF01404633 |
| [12] | Ivanov D.N., Moscow Univ. Math. Bull 44 (2) pp 59– (1989) |
| [13] | Kac V.G., Infinite dimensional Lie algebras; an introduction (1983) · Zbl 0537.17001 |
| [14] | Koshitani S., Commun. Algebra 15 pp 1215– (1987) · Zbl 0634.20018 · doi:10.1080/00927878708823466 |
| [15] | Kostrikin A.I., Soviet Math. Dokl 24 pp 292– (1981) |
| [16] | Kostrikin A.I., Soviet Math. Dokl 25 pp 23– (1982) |
| [17] | Kostrikin A.I., Proc. Steklov Inst. Math 3 pp 85– (1985) |
| [18] | Kostrikin A.I., Soviet Math. Dokl 42 pp 538– (1991) |
| [19] | Kostrikin A.I., Orthogonal Decompositions and Integral Lattics (1993) |
| [20] | Sah C.H., J. Algebra 45 pp 17– (1977) · Zbl 0352.18021 · doi:10.1016/0021-8693(77)90360-X |
| [21] | Seitz G.M., On the minimal degrees of projective representations 45 (1977) |
| [22] | Smith P.E., Bull. London Math. Soc 8 pp 161– (1976) · Zbl 0348.20015 · doi:10.1112/blms/8.2.161 |
| [23] | Thompson J.G., J. Algebra 38 pp 525– (1976) · Zbl 0361.20027 · doi:10.1016/0021-8693(76)90235-0 |
| [24] | Thompson, J.G. A simple subgroup of E8(3). Finite Groups, Symposium, N. Iwahori. pp.113–116. Japan Soc. for Promotion of Science. |
| [25] | Huu Tiep Pham, Math. USSR Sbornik 68 pp 257– (1991) · Zbl 0707.17008 · doi:10.1070/SM1991v068n01ABEH002103 |
| [26] | Huu Tiep Pham, Commum. Algebra 19 pp 2729– (1991) · Zbl 0734.17007 · doi:10.1080/00927879108824291 |
| [27] | Huu Tiep Phum, Soviet Math. Dokl 44 pp 75– (1992) |
| [28] | Huu Tiep Pham, Algebra i analiz 4 (5) (1992) · Zbl 0717.17012 |
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