منابع مشابه
Homotopical Nilpotence of S3
In [l] Berstein and Ganea define the nilpotence of an ü-space to be the least integer » such that the »-commutator is nullhomotopic. We prove that S3 with the usual multiplication is 4 nilpotent. Let X be an ii-space. The 2-commutator c2: XXX—>X is defined by c2(x, y) =xyx~1y~1 where the multiplication and inverses are given by the ü-space structure of X. The »-commutator cn: X"-+X is defined i...
متن کاملGravitational Solitons and the Squashed Seven - Sphere
We discuss some aspects of higher-dimensional gravitational solitons and kinks, including in particular their stability. We illustrate our discussion with the examples of (non-BPS) higher-dimensional Taub-NUT solutions as the spatial metrics in (6 + 1) and (8 + 1) dimensions. We find them to be stable against small but non-infinitesimal disturbances, but unstable against large ones, which can l...
متن کاملThe Nilpotence Height of P
The method of Walker and Wood is used to completely determine the nilpotence height of the elements P s t in the Steenrod algebra at the prime 2. In particular, it is shown that (P s t ) 2bs/tc+2 = 0 for all s ≥ 0, t ≥ 1. In addition, several interesting relations in A are developed in order to carry out the proof.
متن کاملSeven Sphere and the Exceptional Nonlinear Superconformal Algebras
The realizations of the exceptional non-linear (quadratically generated, or W type) N = 8 and N = 7 superconformal algebras with Spin(7) and G2 affine symmetry currents are reviewed. Both the N = 8 and N = 7 algebras admit unitary realizations in terms of a single boson and free fermions in 8 of Spin(7) and 7 of G2, with the central charges c8 = 26/5 and c7 = 5, respectively. They can also be r...
متن کاملSuperconformal Chern - Simons Theories and the Squashed Seven Sphere
We show that there are two supersymmetric completions of the three-dimensional Chern-Simons theory of level k with gauge group U(N) × U(N) coupled to four sets of massless scalars and spinors in the bi-fundamental representation, if we require Sp(2) ⊂ SU(4) global symmetry with the matter fields in the fundamental representation of SU(4). One is the N = 6 superconformal theory recently studied ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1972
ISSN: 0002-9939
DOI: 10.2307/2037872