56 research outputs found
Invariant Tensors Formulae via Chord Diagrams
We provide an explicit algorithm to calculate invariant tensors for the
adjoint representation of the simple Lie algebra , as well as arbitrary
representation in terms of roots. We also obtain explicit formulae for the
adjoint representations of the orthogonal and symplectic Lie algebras
and .Comment: 18 pages, 8 figures. To appear in a special issue of Journal of
Mathematical Science
Photography principle, data transmission, and invariants of manifolds
In the present paper we develop the techniques suggested in
\cite{ManturovNikonov} and the photography principle \cite{ManturovWan} to open
a very broad path for constructing invariants for manifolds of dimensions
greater than or equal to 4
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