92 research outputs found
Note on Moufang-Noether currents
The derivative Noether currents generated by continuous Moufang
tranformations are constructed and their equal-time commutators are found. The
corresponding charge algebra turns out to be a birepresentation of the tangent
Mal'ltsev algebra of an analytic Moufang loop.Comment: LaTeX2e, 6 pages, no figures, presented on "The XVth International
Colloquium on Integrable Systems and Quantum Symmetries, Prague, 15-17 June,
2006
Octonionic representations of Clifford algebras and triality
The theory of representations of Clifford algebras is extended to employ the
division algebra of the octonions or Cayley numbers. In particular, questions
that arise from the non-associativity and non-commutativity of this division
algebra are answered. Octonionic representations for Clifford algebras lead to
a notion of octonionic spinors and are used to give octonionic representations
of the respective orthogonal groups. Finally, the triality automorphisms are
shown to exhibit a manifest \perm_3 \times SO(8) structure in this framework.Comment: 33 page
The Seven-sphere and its Kac-Moody Algebra
We investigate the seven-sphere as a group-like manifold and its extension to
a Kac-Moody-like algebra. Covariance properties and tensorial composition of
spinors under are defined. The relation to Malcev algebras is
established. The consequences for octonionic projective spaces are examined.
Current algebras are formulated and their anomalies are derived, and shown to
be unique (even regarding numerical coefficients) up to redefinitions of the
currents. Nilpotency of the BRST operator is consistent with one particular
expression in the class of (field-dependent) anomalies. A Sugawara construction
is given.Comment: 22 pages. Macropackages used: phyzzx, epsf. Three epsf figure files
appende
Non-Desarguian geometries and the foundations of geometry from David Hilbert to Ruth Moufang
In this work, we study the development of non-Desarguian geometry from David Hilbert to Ruth Moufang. We will see that a geometric model became a complicated interrelation between algebra and geometr
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