Corrections and additions to "Pieces of 2d: Existence and uniqueness for Barnes-Wall and Ypsilanti lattices" [Adv. Math. 196 (2005) 147-192] (DOI:10.1016/j.aim.2004.08.014);Pieces of 2d: Existence and uniqueness for Barnes-Wall and Ypsilanti lattices

Advances in Mathematics

Volumn 196, Issue 1, 2005, Pages 147-192

  Griess Jr , Robert L ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Barnes Wall Lattices; Isometry groups; Lattices; Uniqueness

Indexed keywords

EID: 23644457767     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2006.09.003     Document Type: Erratum

References (30)

1. E. Bannai Positive definite unimodular lattices with trivial automorphism groups Mem. Amer. Math. Soc. 85 429 1990 MR1004770 (90j:11030)
2. E.S. Barnes G.E. Wall Some extreme forms defined in terms of abelian groups J. Amer. Math. Soc. 1 1959 47-63
3. B. Bolt T.G. Room G.E. Wall On the Clifford collineations, transform and similarity groups, I J. Austral. Math. Soc. 2 1961 60-79
4. B. Bolt, T.G. Room, G.E. Wall, On the Clifford collineations, transform and similarity groups, II, J. Austral. Math. Soc. (1961) 80-96.
5. B. Bolt, T.G. Room, G.E. Wall, On the Clifford collineations, transform and similarity groups, III; generators and relations, J. Austral. Math. Soc. (1961).
6. N. Bourbaki, Élements de Mathématique, Groupes et algèbres de Lie, Chapitres 2 et 3, Diffusion C.C. L. S., Paris, 1972.
7. eme Série, t. 6 1973 17-52
8. R. Carter Simple Groups of Lie Type 1972 Wiley-Interscience London
9. J. Conway N. Sloane Self-dual codes over the integers modulo 4 J. Combin. Theory, Ser. A 62 1993 30-45
10. C. Curtis I. Reiner Representation Theory of Groups and Associative Algebras 1962 Interscience
11. C. Dong R. Griess Jr. G. Hoehn Framed vertex operator algebras, codes and the moonshine module Commun. Math. Phys. 193 1998 407-448
12. D. Gorenstein Finite Groups 1968 Harper and Row New York
13. R.L. Griess Jr. Automorphisms of extra special groups and nonvanishing degree 2 cohomology Pacific J. Math. 48 1973 403-422
14. 8) J. Algebra 40 1976 271-279
15. R.L. Griess Jr., The monster and its nonassociative algebra, in: Proceedings of the Montreal Conference on Finite Groups, Contemporary Mathematics, vol. 45, American Mathematical Society, Providence, RI, 1985, pp. 121-157.
16. R.L. Griess Jr. Sporadic groups code loops and nonvanishing cohomology J. Pure Appl. Algebra 44 1987 191-214
17. R.L. Griess Jr. Elementary abelian subgroups of algebraic groups Geom. Dedicata 39 1991 253-305
18. R.L. Griess Jr. Twelve Sporadic Groups 1998 Springer Berlin
19. R.L. Griess Jr. Pieces of Eight Adv. in Math. 148 1999 75-104
20. R.L. Griess Jr. Positive definite lattices of rank at most 8 J. Number Theory 103 2003 77-84
21. B. Gross Group representations and lattices J. Amer. Math. Soc. 3 4 1990 929-960
22. B. Huppert Endliche Gruppen I 1968 Springer Berlin
23. O. King A mass formula for unimodular lattices with no roots (English. English summary) Math. Comput. 72 242 2003 839-863 (electronic) 11H55 (11E41) MR1954971 (Review)
24. M. Kneser Theorie der Kristalgitter Math. Ann. 127 1954 105-106
25. J. MacWilliams N. Sloane The Theory of Error Correcting Codes 1977 North-Holland Amsterdam
26. J. Milnor D. Husemoller Symmetric Bilinear Forms, Ergebnisse der Mathematick und Ihrer Grenzgebiete, Band 73 1973 Springer New York
27. H. Minkowski Zur Theorie der positiven quadratischen Formen J. Reine Angew. Math. 101 1887 196-202
28. I. Niven H.S. Zuckerman H.L. Montgomery An Introduction to the Theory of Numbers fifth ed. 1991 Wiley New York
29. B.L. Rothschild J.H. van Lint Characterizing finite subspaces J. Combin. Theory 16A 1974 97-110
30. J.P. Serre, A Course in Arithmetic, Graduate Texts in Mathematics, vol. 7, Springer, Berlin, 1973.