ABSTRACT
This paper proposes a mathematical framework to construct non-degenerate invariant bilinear forms for E11 semidirect product representations, resolving degeneracy issues in quantum theories.
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Key findings
E11 is a compelling candidate for the fundamental symmetry underlying M-theory.
Proposes a rigorous mathematical framework for constructing non-degenerate invariant bilinear forms.
Leveraging root space decomposition and quadratic Lie algebra theory to extend the invariant form.
Explicit construction algorithms provided, with analysis of resulting algebraic structures.
Limitations & open questions
Further research needed to fully explore the implications of the constructed forms in M-theory.