Simultaneous mutually commuting coset Virasoro actions are realized on the tensor algebra of the Feingold-Frenkel algebra, giving explicit decompositions and tensor ground states up to level five.
Complexity and the Big Bang
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After a brief review of current scenarios for the resolution and/or avoidance of the Big Bang, an alternative hypothesis is put forward implying an infinite increase in complexity towards the initial singularity. This may result in an effective non-calculability which would present an obstruction to actually reaching the beginning of time. This proposal is motivated by the appearance of certain infinite-dimensional duality symmetries of indefinite Kac--Moody type in attempts to unify gravity with the fundamental matter interactions, and deeply rooted in properties of Einstein's theory.
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From Tensor Algebras to Hyperbolic Kac-Moody Algebras
Simultaneous mutually commuting coset Virasoro actions are realized on the tensor algebra of the Feingold-Frenkel algebra, giving explicit decompositions and tensor ground states up to level five.